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<img src="data:image/png;base64,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" class="Wirisformula" alt="R equals fraction numerator u to the power of 2 end exponent sin invisible function application 2 theta over denominator g end fraction equals fraction numerator 2 u subscript x end subscript v subscript y end subscript over denominator g end fraction" width="169" height="42" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»R«/mi»«mo»=«/mo»«mfrac»«mrow»«msup»«mrow»«mi»u«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mn»2«/mn»«mi»θ«/mi»«/mrow»«/mrow»«/mrow»«mrow»«mi»g«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»2«/mn»«msub»«mrow»«mi»u«/mi»«/mrow»«mrow»«mi»x«/mi»«/mrow»«/msub»«msub»«mrow»«mi»v«/mi»«/mrow»«mrow»«mi»y«/mi»«/mrow»«/msub»«/mrow»«mrow»«mi»g«/mi»«/mrow»«/mfrac»«/math»'/> <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAKCAYAAABSfLWiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAACBJREFUeNpjYCAM/kMxRYAqhowC/AEZAJVbThdDBgYAAO75C+VyngYIAAAAUHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4mI3gyMjM0OzwvbW8+PC9tYXRoPhpvPpoAAAAASUVORK5CYII=" class="Wirisformula" alt="therefore" width="17" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»∴«/mo»«/math»'/> Range <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAJCAYAAAA7KqwyAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAIzv8arAAAAHJJREFUeNpjYMAEBUB8C4pPArEbVFwciFcB8TcGPKAaiOcCMROUbw3Er6HiV6CGs+Az4BMQ86CJBQHxfyCOZSACfAFiURwGRBJjQC0Qr0NyhSXUC2lAfA6I84CYjZAhRUD8GOodkL9DkQJxExD/YBheAACBnReBU+gAnQAAAFB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjIxRDs8L21vPjwvbWF0aD5YhjxOAAAAAElFTkSuQmCC" class="Wirisformula" alt="proportional to" width="16" height="9" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»∝«/mo»«/math»'/> horizontal initial velocity <img src="data:image/png;base64,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" class="Wirisformula" alt="left parenthesis u subscript x end subscript right parenthesis" width="29" height="19" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»(«/mo»«msub»«mrow»«mi»u«/mi»«/mrow»«mrow»«mi»x«/mi»«/mrow»«/msub»«mo»)«/mo»«/math»'/> In path 4 range is maximum so football possess maximum horizontal velocity in the path

Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to initial horizontal velocity component, highest first <img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905880/1/912384/Picture507.png" alt="" width="194" height="104" />

Solution for the question - figure shows four paths for a kicked football. ignoring the effects of airon the flight, rank the paths according to initial horizon

Figure shows four paths for a kicked football. ignoring the eff-Turito

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The forces acting on the ball will be (i) in the direction opposite to its motion <math xmlns="http://www.w3.org/1998/Math/MathML" ><mi>i</mi><mi>e</mi><mo>,</mo></math> frictional force and(ii) weight <math xmlns="http://www.w3.org/1998/Math/MathML" ><mi>m</mi><mi>g</mi></math>.

A boy throws a cricket ball from the boundary to the wicket-keeper. If the frictional force due to air cannot be ignored, the forces acting on the ball at the position X are respected by
<img src="data:image/png;base64,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" alt="" />

Solution for the question - a boy throws a cricket ball from the boundary to the wicket-keeper. if thefrictional force due to air cannot be ignored, the forces

A boy throws a cricket ball from the boundary to the wicket-kee-Turito

Displacement <img src="data:image/png;base64,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" class="Wirisformula" alt="equals A B" width="38" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»=«/mo»«mi»A«/mi»«mi»B«/mi»«/math»'/> angle between <img src="data:image/png;base64,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" class="Wirisformula" alt="stack r subscript 1 end subscript with rightwards arrow on top" width="16" height="26" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mover accent=¨true¨»«mrow»«msub»«mrow»«mi»r«/mi»«/mrow»«mrow»«mn»1«/mn»«/mrow»«/msub»«/mrow»«mo»→«/mo»«/mover»«/math»'/> and <img src="data:image/png;base64,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" class="Wirisformula" alt="stack r subscript 2 end subscript with rightwards arrow on top" width="16" height="26" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mover accent=¨true¨»«mrow»«msub»«mrow»«mi»r«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msub»«/mrow»«mo»→«/mo»«/mover»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="theta equals 75 degree minus 15 degree equals 60 degree" width="140" height="14" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»θ«/mi»«mo»=«/mo»«mn»75«/mn»«mo»°«/mo»«mo»-«/mo»«mn»15«/mn»«mo»°«/mo»«mo»=«/mo»«mn»60«/mn»«mo»°«/mo»«/math»'/> From figure <img src="data:image/png;base64,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" class="Wirisformula" alt="A B to the power of 2 end exponent equals r subscript 1 end subscript superscript 2 end superscript plus r subscript 2 end subscript superscript 2 end superscript minus 2 r subscript 1 end subscript r subscript 2 end subscript c o s theta" width="191" height="23" style="vertical-align:-7px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»A«/mi»«msup»«mrow»«mi»B«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»=«/mo»«msubsup»«mrow»«mi»r«/mi»«/mrow»«mrow»«mn»1«/mn»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msubsup»«mo»+«/mo»«msubsup»«mrow»«mi»r«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msubsup»«mo»-«/mo»«mn»2«/mn»«msub»«mrow»«mi»r«/mi»«/mrow»«mrow»«mn»1«/mn»«/mrow»«/msub»«msub»«mrow»«mi»r«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msub»«mi»c«/mi»«mi»o«/mi»«mi»s«/mi»«mi»θ«/mi»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="equals 3 to the power of 2 end exponent plus 4 to the power of 2 end exponent minus 2 cross times 3 cross times 4" width="151" height="17" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»=«/mo»«msup»«mrow»«mn»3«/mn»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»+«/mo»«msup»«mrow»«mn»4«/mn»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»-«/mo»«mn»2«/mn»«mo»×«/mo»«mn»3«/mn»«mo»×«/mo»«mn»4«/mn»«/math»'/> cos<img src="data:image/png;base64,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" class="Wirisformula" alt="60 degree" width="26" height="14" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mn»60«/mn»«mo»°«/mo»«/math»'/> <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACUAAAANCAYAAAAuYadYAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAKVJREFUeNpjYKA+UAPiWiC+gEPeEYi3AfE3IP4BxLeAeAIQCzPQECwG4jQg/o9Dfj8QBwExG5KYARDvYKAD+E+i+k+DzVFKQHyDkGGEMLUcJQ7EidB05TXQIYXuyQIGOgFiQkoQiAOA+CQQ2w+W6IMBHqjDBl3u+zHYHKUHTewD5qiDQBwKxCxAzAQt4e8DcTytHYMvDdoC8RZodP2AlvA+DIMdAAAh/zx2gau2TgAAAFR0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+PTwvbW8+PG1uPjEzPC9tbj48L21hdGg+ZW+DIAAAAABJRU5ErkJggg==" class="Wirisformula" alt="equals 13" width="37" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»=«/mo»«mn»13«/mn»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="A B equals square root of 13" width="74" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»A«/mi»«mi»B«/mi»«mo»=«/mo»«msqrt»«mn»13«/mn»«/msqrt»«/math»'/>

In a two dimensional motion of a particle, the particle moves from point <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAANCAYAAACdKY9CAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIdJREFUeNpjYMAPChhIAOFA/AuIWYhRLAjEl4B4NxAHEKNhJhBHAnE8EE8hpNgSiLdA2eJAfBefYpB7zwCxLJLYOSDWwKWhHohL0MRagTgLm2INqGnowB6IN2HTcBiI/+PAGMGbBsQT8PhtORB7wTiS0DDnwaMhGdnAVUDsQyCopYH4FgM5AACEKxqdNkqvogAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+QTwvbWk+PC9tYXRoPkHiA+IAAAAASUVORK5CYII=" class="Wirisformula" alt="A" width="12" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»A«/mi»«/math»'/>, position vector <img src="data:image/png;base64,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" class="Wirisformula" alt="stack r with rightwards arrow on top subscript 1 end subscript" width="20" height="20" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msub»«mrow»«mover accent=¨true¨»«mrow»«mi»r«/mi»«/mrow»«mo»→«/mo»«/mover»«/mrow»«mrow»«mn»1«/mn»«/mrow»«/msub»«/math»'/>. If the magnitudes of these vectors are respectively, <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAOCAYAAAAmL5yKAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAG1JREFUeNpjYECAeiAuB+IMID4DxD+gfKLBKiB+CsQ9QKzEQAa4BcRBDGQCJiD+xkABMAfi/ZQYEAnE8wmoUQPiWiC+gE1yEhAnEzBgMRCnAfF/bJLrgNiLSNdiNeAdEHNQYgApYCQb8B8LZgAAJQQbPDwRBM8AAABgdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdWI+PG1pPnI8L21pPjxtbj4xPC9tbj48L21zdWI+PC9tYXRoPt1k61AAAAAASUVORK5CYII=" class="Wirisformula" alt="r subscript 1 end subscript" width="16" height="14" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msub»«mrow»«mi»r«/mi»«/mrow»«mrow»«mn»1«/mn»«/mrow»«/msub»«/math»'/>=3 and <img src="data:image/png;base64,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" class="Wirisformula" alt="r subscript 2 end subscript equals 4" width="43" height="17" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msub»«mrow»«mi»r«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msub»«mo»=«/mo»«mn»4«/mn»«/math»'/> and the angles they make with the <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAAKCAYAAABi8KSDAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAHFJREFUeNpjYECAZCDuYMAEzVA5DHAOiMWR+IlAPIUBB/AA4j4o2wWI9zIQALuB2B6ILwCxMCHFBUD8C4j1CCm0BuI1UKdE4lOoBMSbgJgLiHmA+AwuZ4gC8TY0SR8gXoyukA2I1wGxNBZDlkNDiHQAAJxHEBolHuC4AAAASXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT54PC9taT48L21hdGg+wQ7kJQAAAABJRU5ErkJggg==" class="Wirisformula" alt="x" width="11" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»x«/mi»«/math»'/>-axis are <img src="data:image/png;base64,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" class="Wirisformula" alt="theta subscript 1 end subscript equals 75 degree" width="62" height="18" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msub»«mrow»«mi»θ«/mi»«/mrow»«mrow»«mn»1«/mn»«/mrow»«/msub»«mo»=«/mo»«mn»75«/mn»«mo»°«/mo»«/math»'/> and 15<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAYAAAAOCAYAAAAMn20lAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAANvpXuIwAAAC9JREFUeNpjYICALCD+AsSfoGw4AAnIArESlA0HINUqQCyPLpEGxB+ggmkMIxoAAFPoCbXia0SnAAAATnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4mI3hCMDs8L21vPjwvbWF0aD5ZBw9sAAAAAElFTkSuQmCC" class="Wirisformula" alt="degree" width="6" height="14" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»°«/mo»«/math»'/>, respectively, then find the magnitude of the displacement vector <img style="font-size: 1rem;" src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486034/1/912281/Picture490.png" alt="" width="158" height="118" />

Solution for the question - in a two dimensional motion of a particle, the particle moves from point a, position vector vec(r)_(1) . if the magnitudes of these

In a two dimensional motion of a particle, the particle moves f-Turito

Change in velocity <img src="data:image/png;base64,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" class="Wirisformula" alt="equals 2 v sin invisible function application open parentheses theta divided by 2 close parentheses equals 2 v sin invisible function application 20 degree" width="186" height="16" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»=«/mo»«mn»2«/mn»«mi»v«/mi»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mfenced separators=¨|¨»«mrow»«mi»θ«/mi»«mo»/«/mo»«mn»2«/mn»«/mrow»«/mfenced»«mo»=«/mo»«mn»2«/mn»«mi»v«/mi»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mn»20«/mn»«mo»°«/mo»«/mrow»«/mrow»«/mrow»«/mrow»«/math»'/>

A particle is moving on a circular path of radius <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAAKCAYAAACJxx+AAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAFBJREFUeNpjYECAeiAuB+IMID4DxD+gfDhYBcRPgbgHiJUYsIBbQBzEgAMwAfE3BjzAHIj341MQCcTz8SmYBMTJ+BSsA2IvfAreATEHAzkAAA4KDMwPg5X6AAAASXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5yPC9taT48L21hdGg++1GCAwAAAABJRU5ErkJggg==" class="Wirisformula" alt="r" width="8" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»r«/mi»«/math»'/> with uniform velocity <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAKCAYAAABmBXS+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAGpJREFUeNpjYICAICBeyoAJ9gKxF4yjAsQX0BTYA/FJdF3fgJgJiX8ciF3QFYEE9aBsDyA+iMV6hoVAHAplg6y2xKYoC4i7gDgAiHcz4AAgX6wD4itAbIBLERcQ/wDiTQwEwAcg1mEgBwAA5+gQxmAj9O8AAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPnY8L21pPjwvbWF0aD476OiVAAAAAElFTkSuQmCC" class="Wirisformula" alt="v" width="9" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»v«/mi»«/math»'/>. The change in velocity when the particle moves from <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA4AAAANCAYAAACZ3F9/AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIRJREFUeNpjYMAEP4D4PxR/AeJVQOzIQACoAPEFJD4bELsA8X0g1sKnMQCIl2IRTwbiEnwa63Eo6ADiHHwaQf7xQxMTBeJbQCyMTyNIgSQS3xiIjxIKHCYg/gMNzXdQDc1oBmEF5kC8n4EMEAnE88nROAmI08jRuA6IvcjRCAoQDgZaAwA3CRgWSuyN5gAAAFh0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+UDwvbWk+PG1pPiYjeEEwOzwvbWk+PC9tYXRoPguj2AkAAAAASUVORK5CYII=" class="Wirisformula" alt="P blank" width="14" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»P«/mi»«mi» «/mi»«/math»'/>to<img src="data:image/png;base64,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" class="Wirisformula" alt="blank Q blank" width="21" height="14" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi» «/mi»«mi»Q«/mi»«mi» «/mi»«/math»'/>is<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGwAAAAQCAYAAADzhpp3AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAAx5JREFUeNrtWV9km1EU/8RETY2YPsxUmZrZQ4SaqthDmZiZmTG1h5kZMRGzhzIztYcpFXuoPYyYqKopFbOHqlE1MxFlD1M1s5eZPUyNqamIGNm5/MJ1du93z/flJhP640fy5ST3nvu758+9CQI3CsSF4BD/AwtYfzHSxLqnwS8err8zMA6Iv5lINegggjLOeJjMM+Iqe9YktkE10TXitGXTVIh7cGaZeDZkrBzxDbGBMd5bftc3LsMXE44RnxO3wTKe6VC+jRJP4XUHE/DBiQwE6wZqUhvEL8Qx7fk48aP2Pkm8QPzKxJgjviaeIybAq8RvxElLCuH2VyB2todiDRM/hQi2hXno4m4xmwOsyxgTLIBgE65JlIjFLpwYhRNqYin2mVr0l4bv3CHO4vUj7EQTppngCvcc9vUeClbG3E2CXUeG4Vgk3tDe54n7ECtv8M3ZR6i0cj6mA1ns6gp2OcdjTRgeIWqTnCZ+tnxXTyEpbXPsOuz3Ecm+kdWixSRYFWnatImqwjGmDBFpXJA4Dt5E7ZgNsVljKUJhBKnzOPGpILo3tQ01L7Q31eO2gDao9dnR0r3J9pdlHZPY1BIkDWnyH/yJ2YY2DGJwKGFOsMJa05qDXVbzTPiuFW6Jvap7R3vQdheZ+FHWsRVhrJZPwYZR7H8IimMCv93G7lNCPdEETED0MBxBiotj7wtpQ1MWVbCmT8GkKfEkGoAdFjU2qO7ubZfhrwr5iiaGy/4ajgOBx5S4ja7OJdieZR2HfKfETUErPIlBNxBlEqjOaMkRgS1HA1FjbX1DYJ/xHGFSkauWS4Oc76bD1dbPIKQXYxyi8w6bdeJty2cPDe37ssO+1KfbirYlul8Yni+xtj4MRYkPYQfnOUyuEMOpV8RLDptxtPW3kPI681mxnLXOoAnR7dOwn+/j9ZItfaoScB9zS+KM+S7C74oOzgEOm/wea1WY9ztcN7S5Q8KDdwX2P3HQnhLUxqZ27VUI+gubYCn40kT6LkcoIeKrqc4urQeDiRl0rR9wCzEyoH5EuvxVuBsM7t8rahc/wBVZbgDnX+L1/i98NeQJ0OsyBwAAALV0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4QTA7PC9taT48bW8+KDwvbW8+PG1pPiYjeDIyMjA7PC9taT48bWk+UDwvbWk+PG1pPk88L21pPjxtaT5RPC9taT48bW8+PTwvbW8+PG1uPjQwPC9tbj48bW8+JiN4QjA7PC9tbz48bW8+KTwvbW8+PC9tYXRoPq760RIAAAAASUVORK5CYII=" class="Wirisformula" alt="blank left parenthesis angle P O Q equals 40 degree right parenthesis" width="108" height="16" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi» «/mi»«mo»(«/mo»«mi»∠«/mi»«mi»P«/mi»«mi»O«/mi»«mi»Q«/mi»«mo»=«/mo»«mn»40«/mn»«mo»°«/mo»«mo»)«/mo»«/math»'/> <img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905851/1/912216/Picture489.png" alt="" width="149" height="124" />

Solution for the question - a particle is moving on a circular path of radius i with uniform velocity v. the change in velocity when the particle moves from p t

A particle is moving on a circular path of radius i with unifor-Turito

From an inclined plane two particles are projected with same speed at same angle <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJNJREFUeNpjYMAE1kC8DoifAvFBIDZnwAHMoQqZoHxRIL6LS/EFIJZGE9sBxHroCl2AeD4WA5YDsRe64GwgDsKiGOQsN3TBa0D8HwcWR1YI8tAnLKZiFQfp3ItFsSkQr8EVZOigHogT0QV5oMGGDASB+BwQs2EL4ytAnAdlawDxcSD2wRUhelDTfwHxJSD2Y6AEAAAtDR3FA6PhyAAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PC9tYXRoPpXIFCkAAAAASUVORK5CYII=" class="Wirisformula" alt="theta" width="11" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»θ«/mi»«/math»'/>, one up and other down the plane as shown in figure, which of the following statements is/are correct? <img style="font-size: 1rem;" src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905855/1/912209/Picture487.png" alt="" width="128" height="100" />

Solution for the question - from an inclined plane two particles are projected with same speed at sameangle theta , one up and other down the plane as shown in

From an inclined plane two particles are projected with same sp-Turito

A string of length <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAANCAYAAACQN/8FAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAFZJREFUeNpjYMAE34CYiYEAUAHiSwxEgAAgXk6MwnogLidG4SqoqQTBLSCWJqQI5NMvxJhmDsT7iVEYCcTziVE4CYgTiVG4Dog9iFH4Doj/48BsDMQCAHlSEYZSh/nGAAAASXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5MPC9taT48L21hdGg+Bs5jnAAAAABJRU5ErkJggg==" class="Wirisformula" alt="L" width="10" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»L«/mi»«/math»'/> is fixed at one end and carries a mass <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAANCAYAAAB2HjRBAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAMNJREFUeNpjYEAFP4DYhQE/AMn/AWImZEEVIP4PxFPwaOQB4odAfAldIgCILwDxczyaZ0LVLEeXqAficiC+AcTmOJwLsrERqg4FrILa3grFyIALiG8BsQGSOhQAkpSG2noDTW4SkoE3oOrgABRy35D4IH9rQNnWQHwFiFmwqAMDkG370QKmHMm5xjjUgUEkEM9HC5yTQDwBzf/o6uB+SkPzxicgvgZ1Li51YLAOiL3QxBYjORefOoZ3QMzBQBgQq44wAAAH+yrmTEDtWAAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+TTwvbWk+PC9tYXRoPttYuhkAAAAASUVORK5CYII=" class="Wirisformula" alt="M" width="15" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»M«/mi»«/math»'/> at the other end. The string makes <img src="data:image/png;base64,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" class="Wirisformula" alt="2 divided by pi" width="34" height="15" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mn»2«/mn»«mo»/«/mo»«mi»π«/mi»«/math»'/> revolutions per <img src="data:image/png;base64,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" class="Wirisformula" alt="s e c o n d" width="56" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»s«/mi»«mi»e«/mi»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»d«/mi»«/math»'/> around the vertical axis through the fixed end as shown in figure , then tension in the string is<img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486030/1/912200/Picture486.png" alt="" width="179" height="128" />

Solution for the question - a string of length l is fixed at one end and carries a mass m at the otherend. the string makes 2//pi revolutions per second around

A string of length l is fixed at one end and carries a mass m a-Turito

A piece of wire is bent in the shape of a parabola <img src="data:image/png;base64,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" class="Wirisformula" alt="y equals k x to the power of 2 end exponent blank left parenthesis y" width="73" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»y«/mi»«mo»=«/mo»«mi»k«/mi»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mi» «/mi»«mo»(«/mo»«mi»y«/mi»«/math»'/>-axis vertical) with a bead of mass <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAKCAYAAAC9vt6cAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAI5JREFUeNpjYECAeiAuB2JxIJ4ExC+B+DkQe0HlBYG4D4jfAfEnIK5kQAOroIacAeJIIGYBYnkgvg/EkkB8EIjDoeKyQPwDahkc3ALivVCbkMFTIJ6NQ1wSxmEC4m9AzIWmiJA4HJgD8X4GTEC0OMjP87EoJFocFOppWBQSLb4OKbrIEgfFLQcWhaSKkw4A8RgiEla1vLMAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPm08L21pPjwvbWF0aD5oJvHsAAAAAElFTkSuQmCC" class="Wirisformula" alt="m" width="16" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»m«/mi»«/math»'/> on it. The bead can side on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAAKCAYAAABi8KSDAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAHFJREFUeNpjYECAZCDuYMAEzVA5DHAOiMWR+IlAPIUBB/AA4j4o2wWI9zIQALuB2B6ILwCxMCHFBUD8C4j1CCm0BuI1UKdE4lOoBMSbgJgLiHmA+AwuZ4gC8TY0SR8gXoyukA2I1wGxNBZDlkNDiHQAAJxHEBolHuC4AAAASXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT54PC9taT48L21hdGg+wQ7kJQAAAABJRU5ErkJggg==" class="Wirisformula" alt="x" width="11" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»x«/mi»«/math»'/>-axis with a constant acceleration <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAKCAYAAACNMs+9AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAHhJREFUeNpjYEAAJiBuBOKXQPwLiC8AsTwDFrAFiCcBsSBU0yogDkBXFAmVQAYLgdgLXeF+ILZEEzuIzepvUOuQ3fsFm/teo/GtgfgcNoVPgZgDiV8LxGuwKWwG4plQK0HuWgrE2xhwgGqoz2uhpr/EFjzYgCgyBwCLfBT3BN8UQgAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+YTwvbWk+PC9tYXRoPvKcSBcAAAAASUVORK5CYII=" class="Wirisformula" alt="a" width="10" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»a«/mi»«/math»'/>. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAMCAYAAACwXJejAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAHtJREFUeNpjYICAuUAczoAJCoC4FcaJB+IuNAVcQHwLiIVhAl5AvApNUT0Q1yILgFRfQeKLAvFdIOZAt/8bErsP6h4McBiIlaAYZAoTNkULgdgPiJcCcSwDDlAADYpLDHhAABD/h5qGE4AkjzMQANuA2BKfAh0g3oJLEgAnFhPGnhq2GgAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+eTwvbWk+PC9tYXRoPhyYPaAAAAAASUVORK5CYII=" class="Wirisformula" alt="y" width="9" height="12" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»y«/mi»«/math»'/>-axis is <img src="data:image/png;base64,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" alt="" />

Solution for the question - a piece of wire is bent in the shape of a parabola y=kx^(2)(y -axisvertical) with a bead of mass is on it. the bead can side on the

A piece of wire is bent in the shape of a parabola y=kx^(2)(y --Turito

For successfully completing the loop, <img src="data:image/png;base64,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" class="Wirisformula" alt="h equals fraction numerator 5 over denominator 4 end fraction R rightwards double arrow R equals fraction numerator 2 h over denominator 5 end fraction equals fraction numerator 2 cross times 5 over denominator 5 end fraction equals 2 c m" width="247" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»h«/mi»«mo»=«/mo»«mfrac»«mrow»«mn»5«/mn»«/mrow»«mrow»«mn»4«/mn»«/mrow»«/mfrac»«mi»R«/mi»«mo»⇒«/mo»«mi»R«/mi»«mo»=«/mo»«mfrac»«mrow»«mn»2«/mn»«mi»h«/mi»«/mrow»«mrow»«mn»5«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»2«/mn»«mo»×«/mo»«mn»5«/mn»«/mrow»«mrow»«mn»5«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mn»2«/mn»«mi»c«/mi»«mi»m«/mi»«/math»'/>

A frictionless track <img src="data:image/png;base64,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" class="Wirisformula" alt="A B C D E" width="55" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»A«/mi»«mi»B«/mi»«mi»C«/mi»«mi»D«/mi»«mi»E«/mi»«/math»'/> ends in a circular loop of radius <img src="data:image/png;base64,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" class="Wirisformula" alt="R comma" width="16" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»R«/mi»«mo»,«/mo»«/math»'/> figure. A body slides down the track from point <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAANCAYAAACdKY9CAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIdJREFUeNpjYMAPChhIAOFA/AuIWYhRLAjEl4B4NxAHEKNhJhBHAnE8EE8hpNgSiLdA2eJAfBefYpB7zwCxLJLYOSDWwKWhHohL0MRagTgLm2INqGnowB6IN2HTcBiI/+PAGMGbBsQT8PhtORB7wTiS0DDnwaMhGdnAVUDsQyCopYH4FgM5AACEKxqdNkqvogAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+QTwvbWk+PC9tYXRoPkHiA+IAAAAASUVORK5CYII=" class="Wirisformula" alt="A" width="12" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»A«/mi»«/math»'/> which is at a height <img src="data:image/png;base64,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" class="Wirisformula" alt="h equals 5 blank" width="43" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»h«/mi»«mo»=«/mo»«mn»5«/mn»«mi» «/mi»«/math»'/>cm. Maximum value of <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJ5JREFUeNpjYMAEP4D4PxA/BeKTQLwNiEWxqGNQAeILaGKtQNyFTXEAEC9FEwsH4vnYFNcDcQmaWCMQF2BTvAqI/ZD4fEB8A4jFsSm+BcSSQMwCxB5AfA6IQ7EpZALiP9CQgGFbBhzAHIj3I/EtcYUCCERi8fVuIJbHpngSEKehiYFMX4hN8Tog9sIivheItdAF3wExBxbFltAoJw0AAKDiG/NA/rdGAAAASXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5SPC9taT48L21hdGg+SC/J9gAAAABJRU5ErkJggg==" class="Wirisformula" alt="R" width="11" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»R«/mi»«/math»'/> for the body to successfully complete the loop is <img src="data:image/png;base64,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" alt="" />

Solution for the question - a frictionless track abcde ends in a circular loop of radius r_(j) figure.a body slides down the track from point a which is at a he

A frictionless track abcde ends in a circular loop of radius r_-Turito

Equating the moments about <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJ5JREFUeNpjYMAEP4D4PxA/BeKTQLwNiEWxqGNQAeILaGKtQNyFTXEAEC9FEwsH4vnYFNcDcQmaWCMQF2BTvAqI/ZD4fEB8A4jFsSm+BcSSQMwCxB5AfA6IQ7EpZALiP9CQgGFbBhzAHIj3I/EtcYUCCERi8fVuIJbHpngSEKehiYFMX4hN8Tog9sIivheItdAF3wExBxbFltAoJw0AAKDiG/NA/rdGAAAASXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5SPC9taT48L21hdGg+SC/J9gAAAABJRU5ErkJggg==" class="Wirisformula" alt="R" width="11" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»R«/mi»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="6 cross times P R equals 4 cross times R Q" width="114" height="14" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mn»6«/mn»«mo»×«/mo»«mi»P«/mi»«mi»R«/mi»«mo»=«/mo»«mn»4«/mn»«mo»×«/mo»«mi»R«/mi»«mi»Q«/mi»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="P R equals fraction numerator 4 over denominator 6 end fraction R Q equals fraction numerator 2 over denominator 3 end fraction R Q" width="136" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»P«/mi»«mi»R«/mi»«mo»=«/mo»«mfrac»«mrow»«mn»4«/mn»«/mrow»«mrow»«mn»6«/mn»«/mrow»«/mfrac»«mi»R«/mi»«mi»Q«/mi»«mo»=«/mo»«mfrac»«mrow»«mn»2«/mn»«/mrow»«mrow»«mn»3«/mn»«/mrow»«/mfrac»«mi»R«/mi»«mi»Q«/mi»«/math»'/>

The resultant of a system of forces shown in figure is a force of 10 N parallel to given forces through <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJ5JREFUeNpjYMAEP4D4PxA/BeKTQLwNiEWxqGNQAeILaGKtQNyFTXEAEC9FEwsH4vnYFNcDcQmaWCMQF2BTvAqI/ZD4fEB8A4jFsSm+BcSSQMwCxB5AfA6IQ7EpZALiP9CQgGFbBhzAHIj3I/EtcYUCCERi8fVuIJbHpngSEKehiYFMX4hN8Tog9sIivheItdAF3wExBxbFltAoJw0AAKDiG/NA/rdGAAAASXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5SPC9taT48L21hdGg+SC/J9gAAAABJRU5ErkJggg==" class="Wirisformula" alt="R" width="11" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»R«/mi»«/math»'/>, where <img src="data:image/png;base64,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" class="Wirisformula" alt="P R" width="20" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»P«/mi»«mi»R«/mi»«/math»'/> equals <img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905679/1/912154/Picture483.png" alt="" width="191" height="89" />

Solution for the question - the resultant of a system of forces shown in figure is a force of 10 nparallel to given forces through r , where pr equals (1/2) rq '/>

The resultant of a system of forces shown in figure is a force -Turito

Horizontal component of velocity at <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAANCAYAAACdKY9CAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIdJREFUeNpjYMAPChhIAOFA/AuIWYhRLAjEl4B4NxAHEKNhJhBHAnE8EE8hpNgSiLdA2eJAfBefYpB7zwCxLJLYOSDWwKWhHohL0MRagTgLm2INqGnowB6IN2HTcBiI/+PAGMGbBsQT8PhtORB7wTiS0DDnwaMhGdnAVUDsQyCopYH4FgM5AACEKxqdNkqvogAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+QTwvbWk+PC9tYXRoPkHiA+IAAAAASUVORK5CYII=" class="Wirisformula" alt="A" width="12" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»A«/mi»«/math»'/> <img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/486026/1/912112/Picture550.png" alt="" width="158" height="115" /> <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARwAAAAiCAYAAACN82aJAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAWNPAnzwAABWBJREFUeNrtnFFknFkUx68RURGlD1VVFSqqKqovFRFVy4qKqCpVFdWHkIeqykOp6kMfal9qH1atJSqqDytExKqqJaqqYpVatSpq2Yc+VFWJiqoRIT2n+U97986933x3fN8338z8fxzmu3MzmTnfueeec+69nzGEEJINgyIrVAMhpAjOiPxONRDlpsi1iHZCYmxHX29ZQpvqchZETke0ExJrO7Ql8o1/RfZFtBMSazuvRQaoLlIR+RzRTkis7dCWyDeGRZ5EtBMSazt6/ZTqIsp5kXue9ouBdkJibUf73ae6iPKLyBWn7ZjIO5EpqodkYDva7zLVVV4uiXwSWcfrPLmJ2Ufz7N24/lVkSWSct4JkYDvaNkd1ZY969wU4iqrIA5ETTp+dIr+JPIfMos1G/36/yAG8zpNdIn+KbCDPnkD7msiOkul3JkUf1dltkZdmu1D5RuQWfidpje0cFnlrtvfg9FJt2TANB3PQciyTIs+cfo9FTlnXE2iz0ehGt4IPFOBw2oVzMOyehD5XRR6KHMesa+C4Z0z31KN4hKALUA/+IkW/syJ3Arnwecd5fYSzmaZ6v86k/4gsm/DmMd29epeqav8jBKEf8LiFOX7MVvxRhHtVhNcXnPc1wljF7LnqRB92mP4EIXpte7bNrOMwQiyKjHnaf8B7nY5Pd2mo6fci6gEuGlX+1yD6aaUNxnIDEvteRxwhGEQ+bHMC9YcsjC9JQqTdTn1U5APaKjBM23kOw1CHcD2E6xHnc18EHFEN3UW5N8VvXgvksNr2vkD9tZPDGUGapOzB/XH5OWV9pxU2mKXTSXI2Mf+/9Lbz2cqJlb9Efmzh90m7nVqjhisNIo4JT8Tzh+f3JxUdq3BmS+i7ASc16fTbTPiMDWYDdfRAj/uttr9FDjn9VjExltEGs3I6aZxNbfJr+yME6mCO4PVJ09pdgzFb8bUGsjPhs9Y9EUevqS/U6oyxkpA2bWEgjGOQVJDKqfFdSulwqi2INJqRolPnq07bT45OKwXrLtYGs3A6yymdTRFHCLZykDp0rf0sXr/0pBxFplQxW/G3UnyHtNFGv9kuSq6a7ytRtuPyzWqa0r21rt8HUqodXZJSxXAITtx40vkHDSaIMtlgkQ4n7RGC0tuOzii3MdMvt6CIZhOzFf9DRhGOzXXPQHjkpJwh57WICNFlzHRH0TiGZwmDwV0e120EfQV+t9jjIM2OjdiUqmOOEIyjPvEKs3ZMsSrr52DEbMW/m6KGc8qTPi01CFs3PA75XGCWtovrZ4x/6faeSbfK1W4kzZan8d68571p3OcQ8+b/K6RzntQrT2KPgzQzNpopGnfMEYI+833nbIiinqkSsxVfl7PfYKBX8D3mHCPRVY/DuD6C69GE/z/lCZt7EcpOWTOvhre6d8QtruvfzqBfLwyoU0/SNuNw9kJv/Q3uge2QtEi6huhzl5WmTuB+Z73AEXscJHZsNLss3lFHCHQj2lAJimixW/GPIsrYRP3JjWj071/j814FZpzawNlE+uRbAt+N6OUT+ul3Ox74/nNw4Kqb2QaDq9tYMPUrhy77MFhtBuEE1nGvPiKCzWOvWIwNFjk2uuYIwXBCvs1nqpSfUQzOdQwidcyTVAvHRlntKFREC7WTcvEU96rfmilXOrSuVDTdNDYKs6M7xl8sC7WT8jOAWgrh2CidHYWKZXymSntTpQo4NspoR6GCbRmfqULSMWL4mAOODdoRKQAdCLqyN0pVENoRyRNd8tXDq2NUBaEdkTw5ACMZpCoI7YjkiR7D0I2LfVQFoR2RPNEHW+kO3x6qgtCOSN48NPUPtSKEdkRyoVOfqUPayI6+AEnzCECtj72oAAABlHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtc3ViPjxtaT52PC9taT48bWk+SDwvbWk+PC9tc3ViPjxtbz49PC9tbz48bWk+dTwvbWk+PG1pPmNvczwvbWk+PG1vPiYjeDIwNjE7PC9tbz48bW4+NjA8L21uPjxtbz4mI3hCMDs8L21vPjxtbz49PC9tbz48bWZyYWM+PG1pPnU8L21pPjxtbj4yPC9tbj48L21mcmFjPjxtaT4mI3hBMDs8L21pPjxtbz4mI3gyMjM0OzwvbW8+PG1pPkE8L21pPjxtaT5DPC9taT48bW8+PTwvbW8+PG1zdWI+PG1pPnU8L21pPjxtaT5IPC9taT48L21zdWI+PG1vPiYjeEQ3OzwvbW8+PG1pPnQ8L21pPjxtbz49PC9tbz48bWZyYWM+PG1yb3c+PG1pPnU8L21pPjxtaT50PC9taT48L21yb3c+PG1uPjI8L21uPjwvbWZyYWM+PC9tYXRoPoLn1JkAAAAASUVORK5CYII=" class="Wirisformula" alt="v subscript H end subscript equals u cos invisible function application 60 degree equals fraction numerator u over denominator 2 end fraction blank therefore A C equals u subscript H end subscript cross times t equals fraction numerator u t over denominator 2 end fraction" width="284" height="34" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msub»«mrow»«mi»v«/mi»«/mrow»«mrow»«mi»H«/mi»«/mrow»«/msub»«mo»=«/mo»«mi»u«/mi»«mrow»«mrow»«mi»cos«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mn»60«/mn»«mo»°«/mo»«/mrow»«/mrow»«mo»=«/mo»«mfrac»«mrow»«mi»u«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/mfrac»«mi» «/mi»«mo»∴«/mo»«mi»A«/mi»«mi»C«/mi»«mo»=«/mo»«msub»«mrow»«mi»u«/mi»«/mrow»«mrow»«mi»H«/mi»«/mrow»«/msub»«mo»×«/mo»«mi»t«/mi»«mo»=«/mo»«mfrac»«mrow»«mi»u«/mi»«mi»t«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/mfrac»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="A B equals A C sec invisible function application 30 degree equals fraction numerator u t over denominator 2 end fraction cross times fraction numerator 2 over denominator square root of 3 end fraction equals fraction numerator u t over denominator 2 end fraction" width="247" height="42" style="vertical-align:-19px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»A«/mi»«mi»B«/mi»«mo»=«/mo»«mi»A«/mi»«mi»C«/mi»«mrow»«mrow»«mi»sec«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mn»30«/mn»«mo»°«/mo»«/mrow»«/mrow»«mo»=«/mo»«mfrac»«mrow»«mi»u«/mi»«mi»t«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/mfrac»«mo»×«/mo»«mfrac»«mrow»«mn»2«/mn»«/mrow»«mrow»«msqrt»«mn»3«/mn»«/msqrt»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»u«/mi»«mi»t«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/mfrac»«/math»'/>

The time taken by the projectile to reach from <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAANCAYAAACdKY9CAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIdJREFUeNpjYMAPChhIAOFA/AuIWYhRLAjEl4B4NxAHEKNhJhBHAnE8EE8hpNgSiLdA2eJAfBefYpB7zwCxLJLYOSDWwKWhHohL0MRagTgLm2INqGnowB6IN2HTcBiI/+PAGMGbBsQT8PhtORB7wTiS0DDnwaMhGdnAVUDsQyCopYH4FgM5AACEKxqdNkqvogAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+QTwvbWk+PC9tYXRoPkHiA+IAAAAASUVORK5CYII=" class="Wirisformula" alt="A" width="12" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»A«/mi»«/math»'/> to <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAANCAYAAACQN/8FAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJ5JREFUeNpjYMAEP4D4DxA/BOK7QLwJiCXRFakA8QU0sWYgno+uMACIl6KJBWERY6gH4nI0sYVA7IGucBXUVCYgNgDiuUBcgMUfDLeA+D8Uf8FmEgPUlC9QNhsQuwDxcSBWQ1doDsR70cSigbgLXWEk1E3IIBaIZ6MrnATEiWhic6EGoIB1SI4XBeJQaOCzoSt8h+RjUDQuB2JpBlIBAK5MH2X+n9d5AAAASXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5CPC9taT48L21hdGg+/ChvLAAAAABJRU5ErkJggg==" class="Wirisformula" alt="B" width="10" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»B«/mi»«/math»'/> is <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAOCAYAAAAbvf3sAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAALV/ZLFgAAAG5JREFUeNpjYEAAFSA+ykACCALipcQqrgfi/0i4nBhNq4A4gBQn3QBieWIVMwHxN1JMNwfig6RoiATihaRomADEOaRomALEc3HILYcGNUoIagHxU6gEGzEaCAGQJi9iFRsA8RUgZiFWgzQQi8M4AMktFQfBiVImAAAAU3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT50PC9taT48bW8+LDwvbW8+PC9tYXRoPlJScJcAAAAASUVORK5CYII=" class="Wirisformula" alt="t comma" width="12" height="14" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»t«/mi»«mo»,«/mo»«/math»'/> then the distance <img src="data:image/png;base64,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" class="Wirisformula" alt="A B" width="21" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»A«/mi»«mi»B«/mi»«/math»'/> is equal to <img src="data:image/png;base64,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" alt="" />

Solution for the question - the time taken by the projectile to reach from a to 8 is t then thedistance ab is equal to (ut)/(sqrt3)   (sqrt3)/(2) ut

The time taken by the projectile to reach from a to 8 is t then-Turito

<img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/486055/1/912010/Picture545.png" alt="" width="263" height="121" /> So, <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHsAAAATCAYAAACwYHJIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAA0tJREFUeNrtWVFkHEEYXutERISKiqg64lTkoY5T50QejqiKqCoRq6qqVNSpqFLVh+hDiaiI6FtV5aFCVFVFlIiqE1GqqqpOqT5U9O1EVUQc23/4wmTun929vdndNt2Pj9v/Zmfun++ff/6Zs6wUSeIGcTaivmfRf4q/AKeJWxGPsYlxmlAl5jUvnSF+jGEChonPib+I+xjzUkRj7RFd4jbxHXGNeLzFPtw2hchHPJ8F6NqEp8RJzUsbxNEYxH5LdIjdeB7CpDiGx8kxwfuAOBeT2Hn4ZdIfXX9ViH4IV4jzTOMR4psE012W+MlwnxeIzxTbJAI+Doigqhjs7yLjzwFucnWBEPUF03hLl/djxJ7G/opY8nhvFNuCihnibcV2nzgtPQ8gyHexgt0AK/vgeYL4Db9bZKuTSrvXmG8TPs1Iv0/wjtK+hMx8CBliXbGd84gYv/Tmx6AoaVJUAZMmY4FYlp47id+Zd1eI56XnHmKN2CfZ3ittrIBiT2DlZmG7CsFliJqkw6BPK8hWHDowXhNq6Ex2OJvgiu5E8TTMfPeYEUOk+2MBHP1K7EeAi4D+AJFk7Cp9BRW7rNhsFJsyGpr+wvpU89FpnzMuE8ekVPQwQaGFgy+JZ5nvbGShjJKZfivtuog7zLsNJcuMaPZ1v+LQDViwuQHEDuuTjcC0WhVb7GNT+CxWVG9IodpN4wMQOudxpFCLxiJj4/YrtV3Jowrvxmr7QjxlUGwujYf1qchsE4HS+DhxCZX5vYRW9CAmuMunml5WbBXGNs2cMBym6l73SYN3kepNib3ObE1hfXKgmVfNs8F90Yvqe1PZu+NCH4qNjE87sdWsKtH7WblAsGEbVN5dJF5nJsRrwmxNKgwrNnf0CuvTgs8xruJ1f7DDTAZXyI0jxYjjxQlDYq8y4uhS0w+kvh4cRaZgKyNQl5hjiIXj5Zjm4mhIM941zV1DWLG5S5WwPj0iPvGYK/ZSRb5JsnyivIFUmzO8slvZ4wuoVEVw3pKOij8RjJc1Y9Q1WUus7jXmtzRg7zcotu7+IoxPIkC3MQZXB1TbEaRo+Krvf0Wif4QEhRPjteJRh0jTUf3FORdgO/bFoolOUvwb0BU4KY4g6gkdy1K0iT9p6vl4N4BbEAAAAOZ0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXN1Yj48bWk+VjwvbWk+PG1pPnI8L21pPjwvbXN1Yj48bW8+PTwvbW8+PG1uPjI8L21uPjxtaT4mI3gzQzk7PC9taT48bWk+UjwvbWk+PG1pPnNpbjwvbWk+PG1vPiYjeDIwNjE7PC9tbz48bXJvdz48bW8+KDwvbW8+PG1pPiYjeDNDOTs8L21pPjxtaT50PC9taT48bW8+KTwvbW8+PC9tcm93PjwvbWF0aD5Qq2ZIAAAAAElFTkSuQmCC" class="Wirisformula" alt="V subscript r end subscript equals 2 omega R sin invisible function application left parenthesis omega t right parenthesis" width="123" height="19" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msub»«mrow»«mi»V«/mi»«/mrow»«mrow»«mi»r«/mi»«/mrow»«/msub»«mo»=«/mo»«mn»2«/mn»«mi»ω«/mi»«mi»R«/mi»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mo»(«/mo»«mi»ω«/mi»«mi»t«/mi»«mo»)«/mo»«/mrow»«/mrow»«/math»'/> At <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG0AAAATCAYAAACa0IPnAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAAmVJREFUeNrtWUFERFEUHSMjSSQjaREZSYtEkqRFJMlIIhktWsRo0aJFtEjSol2SJJKkRSJJi7ZJkkSLpEWbtGrRJkmSMUz3cobpzZu6//3/n0b/cJh/3//v33/fu/ee/ycUKh60EC9CAYoKm8TRIAz2ECamiJkfmMJ5OkSJj5rxTuIB8Q3X37hc2HNktA5tmN8GKojrxCtwA7Y8xCyWnwaHAZglzmnsZ8QEsRzHTXiGhKFf28SRAmMnxB5L8eF7DeQcx2HLwxBx15JTTu4VRpZFhefXEW8N/RojLmvsXcRTS7EZJq5q7CvqZpxXStWMz44tEKeF57KjWw7n/zT0ixfnUGO/JDZbWjQu970aezfGvmGfOPjLhBkBpY4NOOgzrQ4eusNFmS8hvii2PsMKZBorvn9EY2fbs2q8R2mxgQdijQ8yvxSNu9OFb/eYJ4tri3FhpH8YS6l948OSU7yb332Q+ZXEowKlxQn2iP05/WXJstJOS8t+O5SYXymvli9JUy8k83Wox4LFPAga99oJ/OasrTKcxzRWzwXKY6laHrnZ71jaSQlIa1OZr6IRGVnmkX9xxGIMPtjGAfqoil5ViLCcnLTkFMvZcY9kfjUEVImH/lVBLV4ovc0WhrAJde+Q3yT/moGsNsVhTs9wK/OPkWmSPpURqOMsXolJgWCJo9Rzr6n1MEY85xQ2YwQZn9e++EvCEx4s4vOivQh2sFTmS/uF00VbFFSCNDIi5kOMKrFpPyEQN3K++vwr7AkyXIr2UPCPg+/g9707D3ufVEwFcIFaiBYvxVQyCGtxQSKmAvwxSMSUb/gCU3qnOlgKmmoAAAC/dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPnQ8L21pPjxtbz49PC9tbz48bWk+VDwvbWk+PG1vPi88L21vPjxtbj4yPC9tbj48bW8+LDwvbW8+PG1pPiYjeEEwOzwvbWk+PG1zdWI+PG1pPlY8L21pPjxtaT5yPC9taT48L21zdWI+PG1vPj08L21vPjxtbj4wPC9tbj48L21hdGg+BNU+4QAAAABJRU5ErkJggg==" class="Wirisformula" alt="t equals T divided by 2 comma blank V subscript r end subscript equals 0" width="109" height="19" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»t«/mi»«mo»=«/mo»«mi»T«/mi»«mo»/«/mo»«mn»2«/mn»«mo»,«/mo»«mi» «/mi»«msub»«mrow»«mi»V«/mi»«/mrow»«mrow»«mi»r«/mi»«/mrow»«/msub»«mo»=«/mo»«mn»0«/mn»«/math»'/> So two half cycles will take place

Two identical discs of same radius <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJ5JREFUeNpjYMAEP4D4PxA/BeKTQLwNiEWxqGNQAeILaGKtQNyFTXEAEC9FEwsH4vnYFNcDcQmaWCMQF2BTvAqI/ZD4fEB8A4jFsSm+BcSSQMwCxB5AfA6IQ7EpZALiP9CQgGFbBhzAHIj3I/EtcYUCCERi8fVuIJbHpngSEKehiYFMX4hN8Tog9sIivheItdAF3wExBxbFltAoJw0AAKDiG/NA/rdGAAAASXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5SPC9taT48L21hdGg+SC/J9gAAAABJRU5ErkJggg==" class="Wirisformula" alt="R" width="11" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»R«/mi»«/math»'/> are rotating about their axes in opposite directions with the same constant angular speed <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAKCAYAAABrGwT5AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAKJJREFUeNpjYEAFm4DYkgE3cAHiNdgkjIF4B5rYBCB2ROJzAPF9bJpnA7EfmtglIBZE4rMB8Sd0jUxA/A6IWZDEQOwvaOq4gPgDNifvRxMzxyIGCo+96JoDgHg5mlgOFrECIO5D1+wFxFvQ/HYFiA+jeQ0kpoGuGaT4MdT5fNDoyICKOUJDeSEQl+OKQ2No6IICpAgq5gHEz4H4BhDHMlATAABcNBz1PQWYJAAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0M5OzwvbWk+PC9tYXRoPrE8LrcAAAAASUVORK5CYII=" class="Wirisformula" alt="omega" width="15" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»ω«/mi»«/math»'/>. The discs are in the same horizontal plane. At time <img src="data:image/png;base64,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" class="Wirisformula" alt="t equals 0" width="34" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»t«/mi»«mo»=«/mo»«mn»0«/mn»«/math»'/>, the points <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIVJREFUeNpjYMAEP4D4PxR/AeJVQOyIRR2DChBfQOKzAbELEN8HYi10xQFAvBSLIclAXIIuWI9NEAg6gDgHXRDkPj80MVEgvgXEwuiKQYKSSHxjID6KzYNMQPwHGgrvoIqa0TTDgTkQ72cgEkQC8XxiFU8C4jRiFa8DYi9iFYM8xcFALQAAM/sYFg8AKnAAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPlA8L21pPjwvbWF0aD4oc3y9AAAAAElFTkSuQmCC" class="Wirisformula" alt="P" width="11" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»P«/mi»«/math»'/> and <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAOCAYAAAD0f5bSAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAALtJREFUeNpjYMAO3IB4BxB/A+IfQHwYiB0Z8IAOIN4AxKZAzATFfkD8EoitsWnIA+KZOAwD2XQcXVAWiK9ATcYFPgAxG7JAKxDnMOAHu4HYAFkAZIs8AU0PgZgLxmGChhQ+wAJ1HorAJwKagoB4IbrgNwKBcBTdPwxQUxJxaKgE4i5sEhpA/BiI46HOBQE9IF4MDVmcwByI90OTDgj/B+IsBhJBOBA/B+IzQJwMxKLEauQB4nIgvgZNyAwAqaghgYyCZAkAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPlE8L21pPjwvbWF0aD715aU4AAAAAElFTkSuQmCC" class="Wirisformula" alt="Q" width="13" height="14" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»Q«/mi»«/math»'/> are facing each other as shown in figure. The relative speed between the two points <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIVJREFUeNpjYMAEP4D4PxR/AeJVQOyIRR2DChBfQOKzAbELEN8HYi10xQFAvBSLIclAXIIuWI9NEAg6gDgHXRDkPj80MVEgvgXEwuiKQYKSSHxjID6KzYNMQPwHGgrvoIqa0TTDgTkQ72cgEkQC8XxiFU8C4jRiFa8DYi9iFYM8xcFALQAAM/sYFg8AKnAAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPlA8L21pPjwvbWF0aD4oc3y9AAAAAElFTkSuQmCC" class="Wirisformula" alt="P" width="11" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»P«/mi»«/math»'/> and <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAOCAYAAAD0f5bSAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAALtJREFUeNpjYMAO3IB4BxB/A+IfQHwYiB0Z8IAOIN4AxKZAzATFfkD8EoitsWnIA+KZOAwD2XQcXVAWiK9ATcYFPgAxG7JAKxDnMOAHu4HYAFkAZIs8AU0PgZgLxmGChhQ+wAJ1HorAJwKagoB4IbrgNwKBcBTdPwxQUxJxaKgE4i5sEhpA/BiI46HOBQE9IF4MDVmcwByI90OTDgj/B+IsBhJBOBA/B+IzQJwMxKLEauQB4nIgvgZNyAwAqaghgYyCZAkAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPlE8L21pPjwvbWF0aD715aU4AAAAAElFTkSuQmCC" class="Wirisformula" alt="Q" width="13" height="14" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»Q«/mi»«/math»'/> is <img src="data:image/png;base64,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" class="Wirisformula" alt="V subscript r end subscript" width="18" height="17" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msub»«mrow»«mi»V«/mi»«/mrow»«mrow»«mi»r«/mi»«/mrow»«/msub»«/math»'/> as function of times best represented by <img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486055/1/912010/Picture480.png" alt="" width="252" height="114" />

Solution for the question - two identical discs of same radius r are rotating about their axes inopposite directions with the same constant angular speed co . t

Two identical discs of same radius r are rotating about their a-Turito

A small body of mass <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAKCAYAAAC9vt6cAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAI5JREFUeNpjYECAeiAuB2JxIJ4ExC+B+DkQe0HlBYG4D4jfAfEnIK5kQAOroIacAeJIIGYBYnkgvg/EkkB8EIjDoeKyQPwDahkc3ALivVCbkMFTIJ6NQ1wSxmEC4m9AzIWmiJA4HJgD8X4GTEC0OMjP87EoJFocFOppWBQSLb4OKbrIEgfFLQcWhaSKkw4A8RgiEla1vLMAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPm08L21pPjwvbWF0aD5oJvHsAAAAAElFTkSuQmCC" class="Wirisformula" alt="m" width="16" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»m«/mi»«/math»'/> slides down from the top of a hemisphere of radius <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAgAAAAKCAYAAACJxx+AAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAFBJREFUeNpjYECAeiAuB+IMID4DxD+gfDhYBcRPgbgHiJUYsIBbQBzEgAMwAfE3BjzAHIj341MQCcTz8SmYBMTJ+BSsA2IvfAreATEHAzkAAA4KDMwPg5X6AAAASXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5yPC9taT48L21hdGg++1GCAwAAAABJRU5ErkJggg==" class="Wirisformula" alt="r" width="8" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»r«/mi»«/math»'/>. The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is <img src="data:image/png;base64,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" alt="" />

Solution for the question - a small body of mass 1 slides down from the top of a hemisphere of radius i. the surface of block and hemisphere are frictionless. t

A small body of mass 1 slides down from the top of a hemisphere-Turito

The trajectory of a particle moving in vast maidan is as shown in the figure. The coordinates of a position <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAANCAYAAACdKY9CAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIdJREFUeNpjYMAPChhIAOFA/AuIWYhRLAjEl4B4NxAHEKNhJhBHAnE8EE8hpNgSiLdA2eJAfBefYpB7zwCxLJLYOSDWwKWhHohL0MRagTgLm2INqGnowB6IN2HTcBiI/+PAGMGbBsQT8PhtORB7wTiS0DDnwaMhGdnAVUDsQyCopYH4FgM5AACEKxqdNkqvogAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+QTwvbWk+PC9tYXRoPkHiA+IAAAAASUVORK5CYII=" class="Wirisformula" alt="A" width="12" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»A«/mi»«/math»'/> are <img src="data:image/png;base64,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" class="Wirisformula" alt="open parentheses 0 , 2 close parentheses." width="40" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfenced separators=¨|¨»«mrow»«mn»0,2«/mn»«/mrow»«/mfenced»«mo».«/mo»«/math»'/> The coordinates of another point at which the instantaneous velocity is same as the average velocity between the points are <img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/905502/1/912003/Picture473.png" alt="" width="218" height="109" />

Solution for the question - the trajectory of a particle moving in vast maidan is as shown in thefigure. the coordinates of a position a are (0,2) the coordinat

The trajectory of a particle moving in vast maidan is as shown -Turito

A point mass <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAKCAYAAAC9vt6cAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAI5JREFUeNpjYECAeiAuB2JxIJ4ExC+B+DkQe0HlBYG4D4jfAfEnIK5kQAOroIacAeJIIGYBYnkgvg/EkkB8EIjDoeKyQPwDahkc3ALivVCbkMFTIJ6NQ1wSxmEC4m9AzIWmiJA4HJgD8X4GTEC0OMjP87EoJFocFOppWBQSLb4OKbrIEgfFLQcWhaSKkw4A8RgiEla1vLMAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPm08L21pPjwvbWF0aD5oJvHsAAAAAElFTkSuQmCC" class="Wirisformula" alt="m" width="16" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»m«/mi»«/math»'/> is suspended from a light thread of length <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAAPCAYAAAAyPTUwAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAG1JREFUeNpjYMAE34CYiYEIoALElxiIBAFAvJxYxfVAXE6s4lVQ04kCt4BYmhiFTNCQIAqYA/F+YhVHAvF8YhVPAuI0YhWvA2IvNDFQmP/HFkLvgJiDWMW4wHIsNmIFBkB8BYhZiFEMiiBxGAcAxxwRrjBQef8AAABTdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPmw8L21pPjxtbz4sPC9tbz48L21hdGg+U5m1/QAAAABJRU5ErkJggg==" class="Wirisformula" alt="l comma" width="11" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»l«/mi»«mo»,«/mo»«/math»'/> fixed at<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAANCAYAAABy6+R8AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAKZJREFUeNpjYMAO9IB4LhC/BOJPQLwQiLUY8IBaIN4AxKZAzATFAUD8EIjNsWmoBuKZOAxzBOIL6IJqQHwDajIuAHKqILJADxDnMOAHu4HYFlngChDLE9D0GIj5YByQk74R0MACxB+QBdig7sUHQoF4MbIAyKZfBALhKLYg3wLEiTg0VOKKChVokMdD3Q8CBlAnzcTnbllo8nkHxK+BeCkQWzJQAwAA3MwcdfVeNCMAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPk88L21pPjwvbWF0aD67BA9SAAAAAElFTkSuQmCC" class="Wirisformula" alt="O" width="13" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»O«/mi»«/math»'/>, is whirled in a horizontal circle at constant speed as shown. From your point of view, stationary with respect to the mass, the forces on the mass are<img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486050/1/911820/Picture463.png" alt="" width="165" height="115" />

Solution for the question - a point mass is is suspended from a light thread of length f fixed at0 , iswhirled in a horizontal circle at constant speed as shown

A point mass is is suspended from a light thread of length f fi-Turito

Let <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAKCAYAAABmBXS+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAGpJREFUeNpjYICAICBeyoAJ9gKxF4yjAsQX0BTYA/FJdF3fgJgJiX8ciF3QFYEE9aBsDyA+iMV6hoVAHAplg6y2xKYoC4i7gDgAiHcz4AAgX6wD4itAbIBLERcQ/wDiTQwEwAcg1mEgBwAA5+gQxmAj9O8AAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPnY8L21pPjwvbWF0aD476OiVAAAAAElFTkSuQmCC" class="Wirisformula" alt="v" width="9" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»v«/mi»«/math»'/> be the velocity at the time of collision <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARAAAAC5CAMAAADXsJC1AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAMAUExURf///87OzrW1tUpKUggZEISEhCEhGaWUlPf374Sc74ScxYyUjGtra+be5ubOc+Zz5uZac+Yx5uZaMebOMea15uaUMeaUc3spWubOUuZS5uZaUuaU5uaUUnsIWq3vWkpr3krvWkpara1rlEqtWq2tWkoZrUJrGa0Z761rGUop3krvGUqtGa0plK3vGa2tGa0pGRAZY3ta73sZ74Tv3oTvnHvvWnutWhBrGXsplHvvGXutGa3OWkpK3krOWq1KlEqMWq2MWkJKGa1KGUoI3krOGUqMGa0IlK3OGa2MGa0IGXvOWnuMWhBKGXsIlHvOGXuMGWNaY+bv797W1r3FxVJaUq0pWubOteacteb3xa0IWubOlOaclEJCQjoxMa2tnAAAALW9teYQteYpEBlrjBkpjOYQlOYIEBlKjBkIjLWM5tYQ5tZaENbOENaUEHtzewgACOb3EEIpY0opEK1rzkprjEopjK0pzhApQntrznspzoTO74TOrXtSpUIQOkIIY0oIEK1KzkpKjEoIjK0IzhAIQntKznsIzoTOzoTOjHtShJylnLVrWlLv71Kt71LvrVKtreYxteYpMSlrWuZzteYpcxnv7xmt7xnvrRmtrRlrrRkprRlr7xnvaxmta3trKRkp7xnvKRmtKXspKZRrWlLO71KM71LOrVKMrQhrWuZSteYIcxnO7xmM7xnOrRmMrRlK7xnOaxmMa3tKKRkI7xnOKRmMKXsIKbVKWlLvzlKtzlLvjFKtjOYxlOYIMSlKWuZzlOYpUhnvzhmtzhnvjBmtjBlKrRkIrRlrzhnvShmtSntrCBkpzhnvCBmtCHspCJRKWlLOzlKMzlLOjFKMjAhKWuZSlOYIUhnOzhmMzhnOjBmMjBlKzhnOShmMSntKCBkIzhnOCBmMCHsICLWt5ub3lOb3QvcQ5vdaEPfOEPeUEOb3a7Xv77XvrbXF73NSSrXFlLXvzrXvjK1r761K73tzpbWUvYSlpXNzUikIEEpra0pKY87W74SEnN73///v/wAAAG9MTKwAAAEAdFJOU////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////wBT9wclAAAACXBIWXMAABcRAAAXEQHKJvM/AAAMVUlEQVR4Xu2d3XLbKhCAhQVIM0LvJhCXgHgCdOkXOFe8b6bO2KM5C5Id2fFf2qSVLH3pOPhn2rLeXRZYlmRlZWUmIDE0ViLGoaG1EijfydBaiRC3WswYW9mhtRKRWT60VgK+2g+tlYBQq8GM4YysBjPGyHWEGSPS1WDGcOL40FwJbNLVYMYIaYbWSoAfWDc0VwIbuU5yxwi2TnLPINU6wowx7/XQWglw54bWSoSwNQQZg6o1BBnD2WowZ3i2hiBjRPq2roKMWVeFzjHVGoKM4akfWiuB3K2rQmM6pNYRZoyQfl0FGdF5uRrMGKvWOcwY4chqMCP4ajDnoDX14Qyxrgqd49ed3DNqtsbsZ7h1Y+oMv25Mjcn3VTY0VyKMrSHIGMPWEGRMKf/xCCMKZ6ekov86XTknSuliOhKxP5ZMxvlTC9YHJhJHJ7M7xqufWhXi7MaCZM5F0Mmc78MvrsFiuZbxrX9P7qufMhjoZDk0z9gXThr4EpD7Fbw5pwd4UVX9m/+cn0xXLq8pSG4VJbbM4V9OBQmWokBu/H0ic8uSHb5vY+rU/0tBjJ8fdoMPT1OedGRb5n5X8IxNZD/oe9KVufXw19TH0coygqyAVwt4MF4g5k5qaPV7/w1YzOCxboskKSidSpYw+pb/CJJUb2BChPsJgKmIdVIgvVNCSKy89fS4XCsktcR5UJl+XBEaguQuiG8ScPItk9zS0wZcgHB9gFe9J51hiJNG77uM0g3vSDsI3rTaGEYlTyocXhKKXnM0/wrzG+nKVvrPM+OsBf3nph9U1A66isBRYs1zrhTI3OBhbGetLzuUtlmSRhkJja+ORP8GVP1GzG7bRkl3IZS9VtC5QQs2GMtgFAmlKOlSBU3TkqgI3TsNzlNg1ckGrCzhU9IQTn5rqCMNgBUj5kMoXKcnBQl58m0QAKcaHpQCJ+pBJQJ5FQXSge4wGuSHdDqd9AurmT944klxgIen/7g2SCQKxZGjN5RKoOPACV/5RrU+6agGDZFBQza415DEtTFEBydSb4OMEJ5OirCQ0Kkdxm34ef4PPsojcgzr3qk/BRIEeiooOBXQg6Ah8NJbMxin3YaI1OK3PNcS3IoDq5oInYfOYc0yn2WFLzL48Q8avjjApx0ehIG1kmToD2s+ZkSVqu1BG+5b7IXd4TcOsk+HD3rqaiPDgpTVbuPldBTEOAihFVabrzo1ElQEa60I+hizx7s6hrgUOorUlipTUSqRp5QONpNn21RV0dt4rdR0li475jOKumLbSvvRrydAFFOdZoOpHOEjsXYJF/C0E0IgATNawQU8iOO/0k91+9ZXv4yfI4eQ7IBBjctfmH5pgcik2UgzXgb07hPSD4EixfQL+/7ddL7Vb4RX4MwImEx4UhqN9YUJLA0f8vsPMTQKlAeKj8PAIhFpWLECDRmegwm5hi44A7Ff7DxEHzLQWdnohaYQdcOqENmdWQlM15tF5u3mfJjkFmMNCQIhbocXmEfUHVMfxj4keBEINmvW0GM0vhTy+jieZHHNqkf44WSqSVsdFkiXgzjt5BJ67LjYuPQ4y+qIbquvRfOzZpSufMCmFKVAG+/UeMgtGcUMLWUMth/5/b6pHCNMbtUwEz1RQzS/ELsR7mMBImvYoSBkk19ZxNvoVn95YWCOFKN05X5ydwMeo/mXF4llYal74GMucxUBUcmrH2kuXdg+PHIeh5yxYU4kPLiS7KXHm/N05QzfMplMGqbhzXKjm5C98arY842pmxoCn+v2afQ2e0JfOJq/SFcGH3J8zlGf9Ybq8IuErRS/67Wpdhj3RVXRTQubKZfpyicNKZ1kGXRfMEbCZ1jYXrR4MK/8TTYxJ46kr1Ul4SNmHzj6ECs18zDCcqZNnULg5il80uioM4Gu0A0II2u2r2Q8HXMX++yDhiA9BK++CX4Us6SsqPfVZmRfgtHWMdy80tKrlZdjSh+HcKVQ3FUppQ6vViAelGp2Ec7XMMFpmxeSCP9c9SFqSEdaZ4kzXYK2LHwi5sFdyZfrWNzUfRmJkM/5/dGHcI2dgbHVJ3VTBSM5hGSgz9SOBnk04EdeIlSDSe6nKVzUEIQZuBZLdWmbX6GrpLm2/8zT4xZ3cz/gnwm88p+ntNGH1DgGJ6wxqKnCZ4qrAklKS9SuFwrNPinb3OBX05Wjhmx2vedoPNpGDXG3NIDzval2wbNuw67OrLleLDaLm904hugEozzGY4m6d+CdC0RU2+KYQjZfbpQ2dHFv1+ENiCXkCpqQF7jHDxLPQCbZrx/Lj/87bK6nK/eRKq8oMWmY23YO4jH9zBJIOe+ECHRjDjJEqsIx0qdec+ccmfd3/wycjFeFRpzWQ8TpC48HWF4dfytdufchi+N2uvLZ7v9iuJPfP/iQhXGnUtuDVffX5F515UVqiLtziH2JPsSyO8ugFxlESyCv7sXhFxlES+B+dWWY0A2tpVDfr64cZ7tLgt8ZYUp4z1OE2Hht/dXJ3u9ogGqZalOFX3jn9pL7VwixuBrY0AmdifxhHhSLNf0iul6MxfAHtS/3KsijfbA89kKUj64QijYznTImP83jQ+wuCORjQ/vVsQ+Pv0QnEndzlwAa6hLcAaUgkPfhycuTjbIvbwFOJOSBLALzzHkxAhbzR2vKfHw2ddKUTxWLtbgJp9B/G1FRPZNBirw/89WJtLmxP/EUwrmabUd5wNPl7qrQCNf+iQshUiQ8ncO4XT57hdDha3XcuSXxhAQicXcvDZXYCA3vTBz//mQ/+ZcW3Y1KYzElowgJRTJiXZBsUhWErlP/SLFYznRlSgh+a814+Q665SkBq5vBXOhWAcJLYmmG8lS2k29CqiogjKlj1I+MTY7lGzqCQ30++FgVjCTHruOMOtanOE8aXz31fywNC7XlLB2GCeucjAerPGMsLXjCEWNZMRyryi0mwoa/2G6D6+g0qAgnagb3e5XPHUXO91UTcsnQUMdUSIWEbExSb1kpWONCaoTYV0OPuWx9FgVmd9FI7p49mhTPXiGUcxaiEP7Wd8yFAcdq08lwbeheUxHvmhGDhqBGv6Fagwh9n5LHQHazwMqnRw5BQ+kx0ycnxspJIa1u5/oUvCIIrM9wBum94QJeRlqXvs9idbEI2fQR8vlL6koF4+Zw4qMvJQUMVbRCt5HGzXFbx/dFptIGHTVkdAZ6yhR3dnI/ITUvh/xKng4+Ae3iNDl2uzOqkfv4sm2PYkA6akj6Z9PCv8W1dOXbMG1Pgy6Lad3cilCtDywC2xC1cdf0MQ0K1RyDYZU8nhAQ1D1Yj5sE5fuXQjLXfiTYWd1oiCp8QlpQMl6lMAEAt2mO2zYZhmdWg57YLbxUzOIIADfXSyDfgp2O/oN5FCFrO0zXHFVMgu8Q7FCx7XHMKh2tZJBHkhPKZDoLl/rVYrH1+OOdLfoKmJ0hxICkOBK+yE4S7jw5mCidfEPILDzq37tCaA7uA/ie6sqvw4PUh8XBzw6xr8Aktw+h7jAT0/8eEAuTjXt0tS+mP1n/Lp4wGK+q4/ncBfD4CqGSepjCPbGf9xJcTVfmZZy8c/gNj3FQdktRkSvpytwyGvJyudexfqwPsnh7frVk1tj3T/0UFXUGZvQdTGlrpspkE07Wka9NduZKlxaXIypKVT/xMKE+TK1c0ilt9xMqkf2TkHA0+wzQjyGMT8Npqs5RnqBKsvkfQH6GK5Ncg6siDf6C0zQojw8LfsLG6jEvD2fkMiTjEnvPsN50dai/DwLp7x9YBuZzbIH+CyuetqViWPrL8HJK6QpVfbruxTTxirSqMXW89gg05PnF+LnjHJNVYc/6u8Fp+OVbL3TYd/o4oPvyxHRlnqXnlwIhGgUCYuhisM77KgcLIN8Pq0IoTcelLWPVHF5VInlTIQ7RcTtuAfDieH1gnslRkIHUthYu7D3lUtWoWky+8jhdGY2rcolfO9wXpSod/dpdGHMGsWJoBcT4lthOHMtM8XIR85dIEYeQE7y4d4JqAZjLm9h5NoOMnp9DuE8bzp1fskSupSuHPKihuTQ6JK9tOHM28/pRvw3/dT1DA/3gfcKT5nDLWyzUaNDNI4Y8ZA8uj8tqpyP8VC57/ptkd/L7RbigbGHw9F75+SuVU18c7m4bDFCz6VxA+Xeo5f3sS7awVJFSPtAAEi6yXQ6cSCvQHYRXfmjOgT92eKXSMr37o7ZaSjWLn1R9w4Ut1m4e8PADE+KUXb6ysrKysrKyMgOS5H/T9J9nbgEV4AAAAABJRU5ErkJggg==" alt="" /> Then, <img src="data:image/png;base64,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" class="Wirisformula" alt="u square root of 2 cos invisible function application 45 degree equals v sin invisible function application 60 degree" width="164" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»u«/mi»«msqrt»«mn»2«/mn»«/msqrt»«mrow»«mrow»«mi»cos«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mn»45«/mn»«mo»°«/mo»«/mrow»«/mrow»«mo»=«/mo»«mi»v«/mi»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mn»60«/mn»«mo»°«/mo»«/mrow»«/mrow»«/math»'/> <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQIAAAAuCAYAAADDVhepAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAABlxJREFUeNrtnV1oXEUUxw8hSAl5qNQQSiqGUkqQIgUNWmKRgEgpfQgSwSKhlEooPogPghYtVXwolIJSS160iEgtSK0ipQoiEoqIPmgIIlKRPomUgkopuixqPCd7li7Te+/OzM7XvXN+cGj27u6907kz587Hf88BEHJnFG1tABMEoQE8ifalVIPQVJ5BO51QeU5xmVLjU7SnpbkITWQ32gracEJlorKsoj2SUJnuQvuD/xWERjGCdhVtp4NzbUc7yk7FBTu4bKOJ1NVhtI8Kjs+iXUL7C62FdgXtDbRN0ry8MYN2Hu0GWpvb3FNSLfa8hrbk6FzvoS2C20WxU1zGFKC1gfmS44+j3dFzjBzrZ9K8vLGMtr/nIXEv2ld8TDBkDO1PtAnH53XpCDaz1x+LXFeTaNfRNhh854Y0saDcw9NJwZCX+CkOCTsC4gxPOWLyItpbBp/fivZTyXs0ejhbcPwLtL3SLAeiFevCSwnPTRageifgR+gsFKbuCGYqOlUovkfbo/G5cbSDvE5Q1qm3we3rKLQo+o3044HYxdODKE5gIfHKWShZA9jOQ12ogSMgrqFNBaivooVJWrT8Dap3VVTh0HN9rkMLi0M9r79Ge1T6sjUb2JHOhL7wPrQPalJJ57m8vRwsGZ6m6gjOcpl9QU/pd7jsDyvvHUd7XfM8d6LNcaOs2vqkjn8f/00jjWXpy9ZQnX+M9liMi68EeEK5krNOFQxF34XOdlhdHMEhLrMvXmZHQDqBb5X3aAvzAYt7VzXUp//LEz1taZf0Zyu2shPYFuPi04E8uEs56zKXu8tF8Lcw5cMR0FPzUoA6JzXjfzzXJx5C+xnsxFatPtc5waOHz6U/W0EPOFrAHYlVAFrBPhLgOi7lrFTeYz2vaX1grEaOYNTjmkbR/P19/vtNtFcszkHD/isV75MTvoD2A7gRc+XGOE/No6phL4D/bR7XctZuw+tt7EM1cgRDXOYQvI32Nzey6xpTwGUe5g9zOWd5OnGg4jsjPGL4RPq0FRchzOJxJVd7ho6+KJOz2korN3O5fXZW3z+7bQe6vxvR/kX7EDqLev3YzQ2zxUbTuX0a3yMx1w7p087aWvCfevt8mnYpk7PaSivVJ+paTW9+KC6D3jagkLk38skkmMlZdaWVbXEE2kzz9bZIcxdsGiQtyL1gcLwIUzkrgJ60UhyBGfMZDK37kaMcWrsPV00NaCVzzuB4Ebpy1i460somTw0kRJg/R2Aqh27CvdDuw1WLhbRlNKF53FbO2ouutHIc/C8WNm1EIBQ/+Jouh9buw2Xbh2VbXOpxl3JWXWmlun24ptHpYlhoR7CWsKVCKDl0CvWs24fXKRMUPQjFSkD1uAs5q6m0UhUUydRA0MVEDl33e6Hbh9e5HzrbSyr7uYOrHCg5bitntZFWXuZyy9RAMCUnObRpH4bv4HZlE8Wpe1Y5Ns1z/kMV8y8TOauNtLLoR0fiCPKi6mk8x++d6zOtzEEObdyHabFElYce42EUzSfG+PVpqJYkm8pZbaSVVM5ZcQTiCCwdQU5yaJs+DCehE6yzCy3eUcDKNi+odGWmv0O5OMhUzmo691rkcoI4AmEAcpFD2/ThdSjK7qBRinzJWatClbnuVCFSgaXoCCSsdjwal34uhpzVdUWESAWW4s2TsNrxaGT6udByVtedKkQqsLpMDSSsdhgk/VxinSpUKrA6rRG0pIl5RdLPOeIfh+dyHTuhjHZN6jZaWO2MkPRzjnAZU8F17IQihiFchKJBiBZWOzMk/ZwjfoXOVsmgTIKf2AkqmyBczEJboobVzgjTNgcg6edKIWHSHgfn8RU7QWUvhIlibEvUsNqZ4TL9XPaQbtpFwhAfsROKWIQSrXcCRA+rnRku089lD4mNTBKghoydUMQ58JvpyJYkwmo3lFDp57KGch9e0/hcjNgJRej8DiPWFGtKmpNTQqefy55V6J9qK0bsBJXZhOd4EgPBPaHTz2XP82hnND8bMnaCCk1hjsjtyo5Q6eeyh7bk6FdlE5qfDxE7QeVutJsggpBcCZF+ToBbv7fWIUTsBBUaTbwqtylbQqSfE3jI/gvcCk5Zhe/YCSo7+SaOym3KllDp5wTobOetaA7hQ6UCI4noKt9YIW8k/VxASLCzpPG5ULETaLpyWG6LAJJ+LlnmpQqEnNvc/8skr+SPwbRTAAABxnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtcm93PjxtaT51PC9taT48bXNxcnQ+PG1uPjI8L21uPjwvbXNxcnQ+PC9tcm93PjwvbWZlbmNlZD48bWZlbmNlZCBzZXBhcmF0b3JzPSJ8Ij48bWZyYWM+PG1uPjE8L21uPjxtc3FydD48bW4+MjwvbW4+PC9tc3FydD48L21mcmFjPjwvbWZlbmNlZD48bW8+PTwvbW8+PG1mcmFjPjxtcm93Pjxtc3FydD48bW4+MzwvbW4+PC9tc3FydD48bWk+djwvbWk+PC9tcm93Pjxtbj4yPC9tbj48L21mcmFjPjxtaT4mI3hBMDs8L21pPjxtaT4mI3hBMDs8L21pPjxtaT4mI3hBMDs8L21pPjxtbz4mI3gyMjM0OzwvbW8+PG1pPnY8L21pPjxtbz49PC9tbz48bWZyYWM+PG1uPjI8L21uPjxtc3FydD48bW4+MzwvbW4+PC9tc3FydD48L21mcmFjPjxtaT51PC9taT48L21hdGg+KPc5oAAAAABJRU5ErkJggg==" class="Wirisformula" alt="open parentheses u square root of 2 close parentheses open parentheses fraction numerator 1 over denominator square root of 2 end fraction close parentheses equals fraction numerator square root of 3 v over denominator 2 end fraction blank therefore v equals fraction numerator 2 over denominator square root of 3 end fraction u" width="258" height="46" style="vertical-align:-19px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfenced separators=¨|¨»«mrow»«mi»u«/mi»«msqrt»«mn»2«/mn»«/msqrt»«/mrow»«/mfenced»«mfenced separators=¨|¨»«mrow»«mfrac»«mrow»«mn»1«/mn»«/mrow»«mrow»«msqrt»«mn»2«/mn»«/msqrt»«/mrow»«/mfrac»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«msqrt»«mn»3«/mn»«/msqrt»«mi»v«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/mfrac»«mi» «/mi»«mi» «/mi»«mi» «/mi»«mo»∴«/mo»«mi»v«/mi»«mo»=«/mo»«mfrac»«mrow»«mn»2«/mn»«/mrow»«mrow»«msqrt»«mn»3«/mn»«/msqrt»«/mrow»«/mfrac»«mi»u«/mi»«/math»'/>

A particle is projected from a point <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAANCAYAAACdKY9CAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIdJREFUeNpjYMAPChhIAOFA/AuIWYhRLAjEl4B4NxAHEKNhJhBHAnE8EE8hpNgSiLdA2eJAfBefYpB7zwCxLJLYOSDWwKWhHohL0MRagTgLm2INqGnowB6IN2HTcBiI/+PAGMGbBsQT8PhtORB7wTiS0DDnwaMhGdnAVUDsQyCopYH4FgM5AACEKxqdNkqvogAAAEl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+QTwvbWk+PC9tYXRoPkHiA+IAAAAASUVORK5CYII=" class="Wirisformula" alt="A" width="12" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»A«/mi»«/math»'/> with velocity <img src="data:image/png;base64,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" class="Wirisformula" alt="u square root of 2" width="37" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»u«/mi»«msqrt»«mn»2«/mn»«/msqrt»«/math»'/> at an angle of <img src="data:image/png;base64,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" class="Wirisformula" alt="45 degree" width="26" height="14" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mn»45«/mn»«mo»°«/mo»«/math»'/> with horizontal as shown in figure. It strikes the plane <img src="data:image/png;base64,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" class="Wirisformula" alt="B C" width="21" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»B«/mi»«mi»C«/mi»«/math»'/> at right angles. The velocity of the particle at the time of collision is <img src="data:image/png;base64,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" alt="" />

Solution for the question - a particle is projected from a point a with velocity 4sqrt2 at an angle of45 with horizontal as shown in figure. it strikes the plan

A particle is projected from a point a with velocity 4sqrt2 at -Turito

Assertion: At constant pressure for the change H2O(s)→H2O(g) work done is negative. Reason: During phase transition work done is always negative.

Solution for the question - assertion: atconstantpressureforthe changeh2o(s)h2o(g)workdoneisnegative. reason:duringphasetransitionworkdone isalwaysnegative. if assertion & reason both are false