Turito Academy

Test Prep

Global form fields

The centre of the sphere is (1, 2, –3) so if other extremity of diameter is (x1, y1, z1), then <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator x subscript 1 end subscript plus 2 over denominator 2 end fraction" width="54" height="39" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«msub»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»1«/mn»«/mrow»«/msub»«mo»+«/mo»«mn»2«/mn»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/mfrac»«/math»'/> = 1, <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADQAAAAnCAYAAABAOmveAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAAATJJREFUeNpjYBgaQA2Ia4H4AsMwAYuBOA2I/zMMM0C2h+YCcTgW8QIgbh2KHooH4i40MS4gvgXEwkPRQ15AvApNrB6aMYdkkgPFwhUkvigQ3wViDgocQgjT1EMg8A2J3QfNP0O2UACBw0CsBMWg2GEaBPUDRR5aCMR+QLwUiGMHSf1AkT0F0OL7Eq0topeHAqAG+A0CD5FbiKAAkEeO0yPk6AW2AbHlcPGQDhBvoVfaHlaNxsHoEYoz6ygYBaNg6GTwoYRHwSgYBaOAvsAaiNcA8Scg/gXtpkcPZQ8dBOJIIOaB8rWA+ChUbNgAeSK79EMK/BhOnrGEJrthAUCjriehhcWQB4JAvAGI3YaDZ5SgnlEZDp7RAOLZDJCpmCEPxBkgUzIsw6UQ2AKNoRHRYaQZAAA8s4It0n/8qwAAAJp0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1yb3c+PG1zdWI+PG1pPnk8L21pPjxtbj4xPC9tbj48L21zdWI+PG1vPi08L21vPjxtbj4xPC9tbj48L21yb3c+PG1uPjI8L21uPjwvbWZyYWM+PC9tYXRoPsxlfhoAAAAASUVORK5CYII=" class="Wirisformula" alt="fraction numerator y subscript 1 end subscript minus 1 over denominator 2 end fraction" width="52" height="39" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«msub»«mrow»«mi»y«/mi»«/mrow»«mrow»«mn»1«/mn»«/mrow»«/msub»«mo»-«/mo»«mn»1«/mn»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/mfrac»«/math»'/> = 2, <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator z subscript 1 end subscript plus 1 over denominator 2 end fraction" width="53" height="39" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«msub»«mrow»«mi»z«/mi»«/mrow»«mrow»«mn»1«/mn»«/mrow»«/msub»«mo»+«/mo»«mn»1«/mn»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/mfrac»«/math»'/> = –3 \ Required point is (0, 5, 7). Hence (c) is the correct answer.

<img src="data:image/png;base64,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" class="Wirisformula" alt="Q with dot on top subscript p superscript p left parenthesis cos invisible function application a x minus sin invisible function application b x right parenthesis squared" width="147" height="28" style="vertical-align:-9px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msubsup»«mover accent=¨true¨»«mi»Q«/mi»«mo»§#729;«/mo»«/mover»«mi»p«/mi»«mi»p«/mi»«/msubsup»«mo»(«/mo»«mi»cos«/mi»«mo»§#8289;«/mo»«mi»a«/mi»«mi»x«/mi»«mo»§#8722;«/mo»«mi»sin«/mi»«mo»§#8289;«/mo»«mi»b«/mi»«mi»x«/mi»«msup»«mo»)«/mo»«mn»2«/mn»«/msup»«/math»'/>(where a, b are integers) =

Solution for the question - q^()_(p)(cos ax-sin bx)^(2) (where a, b are integers) = 2il   il  0-id

q^()_(p)(cos ax-sin bx)^(2) (where a, b are integers) = -Turito

PSAT

One-On-One Tutoring

Your gateway to the top global universities

Coding

Discover traits & skills, get a clear pathway to academic success.

Discovery Program

Solution for the question - widehat(0)_(1)^(1)(sin x-x^(2))/(3-|x|)dx= 2 widehat(q)^(1)(sin x-x^(2))/(3-|x|)dx   hat(q)^(1)(-2x^(2))/(3-|x|)dx  2 widehat(q)^(1)(sin x)/(3-|x|)dx

Widehat(0)_(1)^(1)(sin x-x^(2))/(3-|x|)dx= -Turito

Let direction cosines of straight line be l, m, n
\ 4l + m + n = 0
l – 2m + n = 0
Þ <math xmlns="http://www.w3.org/1998/Math/MathML" ><mfrac><mrow><mi>l</mi></mrow><mrow><mn>3</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>m</mi></mrow><mrow><mo>-</mo><mn>3</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mo>-</mo><mn>9</mn></mrow></mfrac></math> Þ <math xmlns="http://www.w3.org/1998/Math/MathML" ><mfrac><mrow><mi>l</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>m</mi></mrow><mrow><mo>+</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></mfrac></math>
\ Equation of straight line is <math xmlns="http://www.w3.org/1998/Math/MathML" ><mfrac><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow><mrow><mo>-</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>y</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>1</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>z</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></math>.
Hence (c) is the correct choice.

<math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mo>&#8747;</mo><mrow><mo>&#8722;</mo><mi>&#960;</mi><mo>/</mo><mn>4</mn></mrow><mrow><mi>&#960;</mi><mo>/</mo><mn>4</mn></mrow></msubsup><mo>&#8202;</mo><mfrac><mrow><msup><mi>e</mi><mi>x</mi></msup><mo>(</mo><mi>x</mi><mi>sin</mi><mo>&#8289;</mo><mi>x</mi><mo>)</mo></mrow><mrow><msup><mi>e</mi><mrow><mn>2</mn><mi>x</mi></mrow></msup><mo>&#8722;</mo><mn>1</mn></mrow></mfrac><mi>d</mi><mi>x</mi></math> is equal to

Solution for the question - int_(-pi//4)^(pi//4)(e^(x)(x sin x))/(e^(2x)-1)dx is equal to 20none of these

Int_(-pi//4)^(pi//4)(e^(x)(x sin x))/(e^(2x)-1)dx is equal to-Turito

Since these two lines are intersecting so shortest distance between the lines will be 0.
Hence (c) is the correct answer.

Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>:</mo><mi>R</mi><mo stretchy="false">&#8594;</mo><mi>R</mi><mo>,</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfenced open="{" close="" separators="|"><mtable columnspacing="1em"><mtr><mtd><mo>|</mo><mi>x</mi><mo>&#8722;</mo><mo>[</mo><mi>x</mi><mo>]</mo><mo>|</mo><mo>,</mo><mo>[</mo><mi>x</mi><mo>]</mo></mtd></mtr><mtr><mtd><mo>|</mo><mi>x</mi><mo>&#8722;</mo><mo>[</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>]</mo><mo>|</mo><mo>,</mo><mo>[</mo><mi>x</mi><mo>]</mo></mtd></mtr></mtable></mfenced></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" columnalign="right left right left right left right left right left right left"><mtr><mtd><mtext>&#160;is odd&#160;</mtext></mtd></mtr><mtr><mtd><mn>1</mn><mtext>&#160;is even where [.]&#160;</mtext></mtd></mtr></mtable></math> denotes greatest integer function, then <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mo>&#8747;</mo><mrow><mo>&#8722;</mo><mn>2</mn></mrow><mn>4</mn></msubsup><mo>&#8202;</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>d</mi><mi>x</mi></math> is equal to

Solution for the question - let f:r rarr r,f(x)={[|x-[x]|","[x]],[|x-[x+1]|","[x]]:} is odd 1 is evenwhere [. denotes greatest integer function, then int_(-2)^(

Let f:r rarr r,f(x)={[|x-[x]|","[x]],[|x-[x+1]|","[x]]:} is o-Turito

Given plane y + z + 1 = 0 is parallel to x-axis as 0.1 + 1.0 + 1.0 = 0
but normal to the plane will be perpendicular to x-axis.
Hence (c) is the correct answer.

The value of <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mo>&#8747;</mo><mn>0</mn><mn>1</mn></msubsup><mo>&#8202;</mo><mo>|</mo><mi>sin</mi><mo>&#160;</mo><mn>2</mn><mi>&#960;</mi><mi>x</mi><mo>|</mo><mo>&#8739;</mo><mi>d</mi><mi>x</mi></math> is equal to

Solution for the question - the value of int_(0)^(1)|sin 2pi x|dx is equal to (1)/(pi)  2(2)/(pi) 0

The value of int_(0)^(1)|sin 2pi x|dx is equal to -Turito

The value of <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGUAAAArCAYAAABhLkbTAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAc1CXO0QAAA8pJREFUeNrtW19IFEEYH44jIkKKSyQqjIijh4igoqIiBAkRCQmjfIiQIiQifAjsIanooZ4MKnqxiAgSpH+ElBByREgUURIRUQ89SIQEJiImYV3fx/1W98bZvR3du5295gc/bnfnbr+5+c18M/PNjBDhI03sIA56pDcQP4ENc0i3mAPuEI8Rs4q07cTnxBSYwbOg6RbzhEqUR8TdrvtdxMca6RZFEGWMmHDdJ/AsaLpFEURRPfutkW5RgpaSLNBSkralFMZS4k3iMGrwPakQdfsUvu7VSLdQoI84RFxDPEn85jNs9Rp9ZSBuJUZa9RrpFor5Axf0YeIqXA9g6CqLIVN+z2fiCIQVmukWLgzAZSVdIyOLCFGBGp+xRWEOGiFKly0Kc3AeorTE+D8s9ujvdGgUepCpOAcID5ab+x2EKOti/B+eEo+WkyiTxKkYj7iWEX/isyzg+OJRQ/KTxsx/QuM3rcSHIdmfgP21mr8JtULvgSh9hojCi181mr/hvqQpxDzUIh9BwOK9D7sQ9kOUbkNE0R0FrSb+IC6MKB+NxSi7VmTgekxFOV1gfnWEeEnx/ALSdPLBrv4KXD33wxywvUZsD8FeHrrETMzLBOiur7wj1hX4zltileu+BYXphynpPgE32YJrjoKcRdk1hmAvD90eL44Cy4kvfQYkMtYTv4uZeJ0XWLROV3/RHyAvr5AfBx1Si3DAwdUVIdjLwxOIUmuI62pWdKS3kLZTSrtIvBzw3c9Ebv2G52SpAN8/ILmwIUXFSPiMEnXt5WEUxisMEKVazF70OgNReB7yWkr7Stwc8N1tcI0bNCprNa43itzaj4ytPlEEXXt5Sk8p/GeU8Kp5x4l/Xb56G/FLANfF2IFOuVPREv0m1A72idzWKhnNqDBh2JtGCq1k2CBRsgUEu4vrq8RzAd7Hq6i8jWkR3M+bgO4kKw17exTfcfbAhWEvr0PKCrP2XvmJcoP4C62D5yaFYnWVcEPuQmnwqPV++eAC/gg3xtgEN8vL5fUh2ZvVmd02SBQ/V7qE+Id432eU5mAB8YFiZOSMOOs081GF903CNkcdRlyT1vnam4azjnLKIFH64S68YkkvkOe2ItlPwH5/VAVg0hzF7QJ4m5PXfrAtyPPKItkfg/3KqAoggz9YLeKFJlHGYP84LiyMQVqYFR3+b1EjZraNnoAoe22xRIcOiNCLEcYHoT6NZU9alRAcz+fI5yGRW+4cU8Rl7EmrEiMJYThW045wgAx70spA2JNWBsKetIpBS7EnrQyAPWllIOxJK0NhT1oVGf8A9n8TQusCg10AAADLdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdWJzdXA+PG1vPiYjeDIyMkI7PC9tbz48bW4+MDwvbW4+PG1uPjEwMDwvbW4+PC9tc3Vic3VwPjxtbz4mI3gyMDBBOzwvbW8+PG1vPns8L21vPjxtc3FydD48bWk+eDwvbWk+PC9tc3FydD48bW8+fTwvbW8+PG1pPmQ8L21pPjxtaT54PC9taT48L21hdGg+EHdN7AAAAABJRU5ErkJggg==" class="Wirisformula" alt="integral subscript 0 superscript 100   left curly bracket square root of x right curly bracket d x" width="101" height="43" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msubsup»«mo»§#8747;«/mo»«mn»0«/mn»«mn»100«/mn»«/msubsup»«mo»§#8202;«/mo»«mo»{«/mo»«msqrt»«mi»x«/mi»«/msqrt»«mo»}«/mo»«mi»d«/mi»«mi»x«/mi»«/math»'/> (where {x} is the fractional part of x) is

Solution for the question - the value of int_(0)^(100)[sqrtx]dx (where {x} is the fractional partof x) is none of these100

The value of int_(0)^(100)[sqrtx]dx (where {x} is the fract-Turito

The shortest distance between the two straight line<img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator x minus 4 divided by 3 over denominator 2 end fraction equals fraction numerator y plus 6 divided by 5 over denominator 3 end fraction equals fraction numerator z minus 3 divided by 2 over denominator 4 end fraction" width="232" height="37" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»x«/mi»«mo»§#8722;«/mo»«mn»4«/mn»«mo»/«/mo»«mn»3«/mn»«/mrow»«mn»2«/mn»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»y«/mi»«mo»+«/mo»«mn»6«/mn»«mo»/«/mo»«mn»5«/mn»«/mrow»«mn»3«/mn»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»z«/mi»«mo»§#8722;«/mo»«mn»3«/mn»«mo»/«/mo»«mn»2«/mn»«/mrow»«mn»4«/mn»«/mfrac»«/math»'/> and <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator 5 y plus 6 over denominator 8 end fraction equals fraction numerator 2 z minus 3 over denominator 9 end fraction equals fraction numerator 3 x minus 4 over denominator 5 end fraction" width="199" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»5«/mn»«mi»y«/mi»«mo»+«/mo»«mn»6«/mn»«/mrow»«mn»8«/mn»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»2«/mn»«mi»z«/mi»«mo»§#8722;«/mo»«mn»3«/mn»«/mrow»«mn»9«/mn»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»3«/mn»«mi»x«/mi»«mo»§#8722;«/mo»«mn»4«/mn»«/mrow»«mn»5«/mn»«/mfrac»«/math»'/> is

Solution for the question - the shortest distance between the two straight lineandis '/>03'/>

The shortest distance between the two straight lineandis -Turito

Velocity of the bob at the point A
<math xmlns="http://www.w3.org/1998/Math/MathML" ><mi>v</mi><mo>=</mo><msqrt><mn>5</mn><mi>g</mi><mi>L</mi></msqrt></math>(i)
<math xmlns="http://www.w3.org/1998/Math/MathML" ><msup><mrow><mfenced separators="|"><mrow><mfrac><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><msup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mn>2</mn><mi>g</mi><mi>h</mi><mfenced separators="|"><mrow><mi>i</mi><mi>i</mi></mrow></mfenced></math>
<math xmlns="http://www.w3.org/1998/Math/MathML" ><mi>h</mi><mo>=</mo><mi>L</mi><mo>(</mo><mn>1</mn><mo>-</mo><mrow><mrow><mi>cos</mi></mrow><mo>⁡</mo><mrow><mi>θ</mi><mo>)</mo></mrow></mrow><mo>(</mo><mi>i</mi><mi>i</mi><mi>i</mi><mo>)</mo></math>
<math xmlns="http://www.w3.org/1998/Math/MathML" ><mi>S</mi><mi>o</mi><mi>l</mi><mi>v</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi> </mi><mi>E</mi><mi>q</mi><mi>s</mi><mo>.</mo><mfenced separators="|"><mrow><mi>i</mi></mrow></mfenced><mo>,</mo><mi> </mi><mfenced separators="|"><mrow><mi>i</mi><mi>i</mi></mrow></mfenced><mi>a</mi><mi>n</mi><mi>d</mi><mi> </mi><mfenced separators="|"><mrow><mi>i</mi><mi>i</mi><mi>i</mi></mrow></mfenced><mo>,</mo><mi> </mi><mi>w</mi><mi>e</mi><mi> </mi><mi>g</mi><mi>e</mi><mi>t</mi></math>
<math xmlns="http://www.w3.org/1998/Math/MathML" ><mrow><mrow><mi>cos</mi></mrow><mo>⁡</mo><mrow><mi>θ</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mn>7</mn></mrow><mrow><mn>8</mn></mrow></mfrac></mrow></mrow></math>
<math xmlns="http://www.w3.org/1998/Math/MathML" ><mi>o</mi><mi>r</mi><mi> </mi><mi> </mi><mi> </mi><mi>θ</mi><mo>=</mo><msup><mrow><mi>c</mi><mi>o</mi><mi>s</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced separators="|"><mrow><mo>-</mo><mfrac><mrow><mn>7</mn></mrow><mrow><mn>8</mn></mrow></mfrac></mrow></mfenced><mo>=</mo><mn>151</mn><mo>°</mo></math>

A bob of mass M is suspended by a massless string of length L. The horizontal velocity <math xmlns="http://www.w3.org/1998/Math/MathML" ><mi>v</mi></math> at position A is just sufficient to make it reach the point B. The angle <math xmlns="http://www.w3.org/1998/Math/MathML" ><mi>θ</mi></math> at which the speed of the bob is half of that at A, satisfies
<img src="data:image/png;base64,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" alt="" />

Solution for the question - a bob of mass _m_ is suspended by a massless string of length _l_. thehorizontal velocity at position _a_ is just sufficient to make

A bob of mass _m_ is suspended by a massless string of length _-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 1 on it. the bead can side on the w

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

A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out length <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAATCAYAAADcZiBNAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAV5JREFUeNpjYBg84D8U/wLiC0DsxjAK8AINIH44Ggz4ARMQvxsNBtxAGIinAHHiaFDgL5diaWw+NjyogAoQH8UjzwfErUCcRqNAGhIgCIiXEqHuBw08T5VAqobWKn+gBpZTOYDq0ZI4LvNtgfjMYAwkUADNBmI2CvM2oTy+CogD8JgJSkE7gFh+MAYSqJxwoUN2u0FiAFA7kECN1U9AvA2Ii4CYhxSLQoH4HBD70bj9843GtRQxtRULEBsDcS000jRIsVwSiA8D8X4CIUyuI82B+OAgq7XcyHETBxBfolFbJRKIFw7Cqv0HOZrmAnE0DTwzAYhzBlkg6QDxXVI1mQLxNWj3gNpgCjQCBiqQ1gGxJbRsBGEPaAAFoalbDjUTpRb+ABX8Ay2PNBhoA7SA+CnULjYG+gNQ5XQL6s930OaIKRZ1WANpFGAPKK/RYMANDID4CrSpMApwAGkgFodxANBhcmlZYhiFAAAAknRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT5zPC9taT48bW8+PTwvbW8+PG1zdXA+PG1pPnQ8L21pPjxtbj4zPC9tbj48L21zdXA+PG1vPis8L21vPjxtbj41PC9tbj48bW8+LDwvbW8+PC9tYXRoPnlSjkkAAAAASUVORK5CYII=" class="Wirisformula" alt="s equals t to the power of 3 end exponent plus 5 comma" width="73" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»s«/mi»«mo»=«/mo»«msup»«mrow»«mi»t«/mi»«/mrow»«mrow»«mn»3«/mn»«/mrow»«/msup»«mo»+«/mo»«mn»5«/mn»«mo»,«/mo»«/math»'/> where <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAKCAYAAABmBXS+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAFtJREFUeNpjYEAF1UD8EIj/APF/IC5nwKJgNhCzMeABR4HYhYEACAXic0DsR0ihJBAfBuL9QMyDTyEHEF8C4lhCJs4F4mh8CkyB+BoQC6NLfICGyx+oezQYSAUA1VgQK/lZBOEAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPnM8L21pPjwvbWF0aD4mx1uGAAAAAElFTkSuQmCC" class="Wirisformula" alt="s" width="9" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»s«/mi»«/math»'/> is in metre and t is in second. The radius of the path is 20 m. The acceleration of P when t =2s is nearly <img src="data:image/png;base64,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" alt="" />

Solution for the question - a point _p_ moves in counter-clockwise direction on a circular path asshown in the figure. the movement of _p_ is such that it sweep

A point _p_ moves in counter-clockwise direction on a circular -Turito

Since these two lines are intersecting so shortest distance between the lines will be 0. Hence (c) is the correct answer.

The equation of the plane containing the line <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator x with not stretchy bar on top minus alpha over denominator 1 end fraction equals fraction numerator y minus beta over denominator m end fraction equals fraction numerator z minus gamma over denominator n end fraction text  is  end text stack a with _ below with _ below left parenthesis x minus alpha right parenthesis plus b left parenthesis y minus beta right parenthesis plus c left parenthesis z minus gamma right parenthesis equals 0" width="428" height="41" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mover accent=¨true¨»«mi»x«/mi»«mo stretchy=¨false¨»§#175;«/mo»«/mover»«mo»§#8722;«/mo»«mi»§#945;«/mi»«/mrow»«mn»1«/mn»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»y«/mi»«mo»§#8722;«/mo»«mi»§#946;«/mi»«/mrow»«mi»m«/mi»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»z«/mi»«mo»§#8722;«/mo»«mi»§#947;«/mi»«/mrow»«mi»n«/mi»«/mfrac»«mtext»§#160;is§#160;«/mtext»«munder accentunder=¨false¨»«munder accentunder=¨false¨»«mi»a«/mi»«mo»_«/mo»«/munder»«mo»_«/mo»«/munder»«mo»(«/mo»«mi»x«/mi»«mo»§#8722;«/mo»«mi»§#945;«/mi»«mo»)«/mo»«mo»+«/mo»«mi»b«/mi»«mo»(«/mo»«mi»y«/mi»«mo»§#8722;«/mo»«mi»§#946;«/mi»«mo»)«/mo»«mo»+«/mo»«mi»c«/mi»«mo»(«/mo»«mi»z«/mi»«mo»§#8722;«/mo»«mi»§#947;«/mi»«mo»)«/mo»«mo»=«/mo»«mn»0«/mn»«/math»'/> where al + bm + cn is equal to

Solution for the question - the equation of the plane containing the line(x-alpha)/(1)=(y-beta)/(m)=(z-gamma)/(pi) is a(x-alpha)+b(y-beta)+c(z-y)=0where al + bm

The equation of the plane containing the line (x-alpha)/(1)=(-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,iVBORw0KGgoAAAANSUhEUgAAAXgAAACKCAMAAACXbqEyAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAMAUExURf////7+/vz8/KGhoTU1NTAwMJWVlXNzcxoaGoqKioKCgoGBgYuLiyIiImJiYnV1dUBAQOnp6ePj4+Tk5Ozs7ExMTGVlZXZ2djs7O9nZ2dfX19zc3N/f30dHR2ZmZtbW1t3d3efn5+jo6O7u7vDw8O/v7/Pz8/X19fT09Pf39/r6+v39/fn5+Xt7ezo6Oubm5ltbWz8/P97e3kZGRm1tbeHh4c/Pz7y8vKmpqZaWloCAgGdnZ1JSUhcXF1FRUerq6u3t7VRUVENDQ8XFxdTU1Li4uJycnFlZWT4+PiMjIwcHBwAAAAEBAXh4eHJycnFxcXBwcH9/f35+fnR0dHp6eikpKS8vL0hISIODg8PDw9jY2MLCwqOjo0FBQQ4ODgMDAxAQEB0dHSoqKjg4OElJSWBgYDw8PDQ0NDc3NyUlJQQEBDIyMjExMRkZGQwMDCEhIbKyssrKyuDg4NDQ0Kenp0JCQg0NDR4eHm9vb4eHh7u7u+Li4uvr64yMjBMTE/Ly8szMzJiYmCcnJxgYGAgICB8fH4iIiNvb26ampl1dXRYWFqurq9HR0URERGpqasbGxpubm25ubgkJCSwsLL29vbq6umtrayYmJgICAiQkJE9PT319fc7Oztra2omJiRQUFKKiopqammxsbD09PQoKCgUFBc3Nzfb29ldXV5eXl8fHx9LS0gYGBtXV1RISElBQUKysrAsLC8HBwRsbG19fX1ZWVlVVVRwcHKSkpOXl5WlpacvLy5+fn6+vr9PT08DAwKCgoFpaWvHx8WhoaLa2tp6enoaGhigoKLW1tfj4+I6Ojr+/v6ioqGFhYWNjY05OToSEhI2NjaWlpUVFRZSUlLm5uXl5eSAgIJKSkrOzszMzM5GRkZmZmcTExA8PD4WFhWRkZLS0tCsrK7CwsK2trXd3d3x8fMnJyZ2dncjIyLGxsbe3t/v7+5CQkK6urlNTU0pKShUVFVxcXF5eXi0tLZOTk6qqqhERETY2No+Pj1hYWDk5Ob6+vi4uLktLSwAAALnhSb4AAAEAdFJOU////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////wBT9wclAAAACXBIWXMAABcRAAAXEQHKJvM/AAALbklEQVR4Xu2dQZKzLBCGcwGuQFnVx/FGrFix4zochmLLFWD7dyNJTMaoMbSZ7x8ek4kaEuNL23QjOpdOp3MSyYsXU6glOizIHIyJ5udTuFqiw0L0MNA0Pe6vFytriQ4L0Q7LdOF5iX7QZOIPDLiuC88LCo9UwSvkbrrwzBSLfxK+W/wJ3Cy+Ll8uRfhu8dzcLP4ySY+vXfgzmFl8Vb4I310NN08WTy/d4s/gZvGke3kWi+/CczO3+Ko9hZPd1XBz9/HkY+gF6RbPz83i5/TGlZ9q8dNUX3DqFs8LgCzCL9CF52HQKoUobXZo3rPHZO4456weSoTZaQUMKkTnxVgQMUoZaYoG/5YHLYhRWBeTGuqnOh+BoifpSfAshLfSSH8FK0LU2YIoNSNcVLqL/xmgU7RFc++iQWOm1rR4F3xcTBaJslaKavChVTDRikziW5O62zkKDMGRihlFT8WNP6KxSuTk32foEG0u4kdVktvOWwAoiZ4jk+1i2L4AGJRXhGflafkqvje6S/8eOpJbFy6Q6D+suqCL4/9p8lV7ZTxKn23o7n43kCz5Cmc0nVx9RcjSO5dDXXwCP6fVVHtS1+/trAKBZLcGQ5PXqpPBu8HGwVJUvwyA1on8lXBd+k0Gkj2ji9FrqiMB207rLiq+MHkCgx10OdgGC5fq93cWGUilLMOqrU8YjFlspCi/rngBlqjS93b2FehkyCWnLWMvUKub0p6SGOEbh/XpVN1O55Ek98s+gVnTLor0eRSm+/qfaCPQKDHfrGI1BooXs6H7m0eKl8GY+z3ZlaozewAVMcKR3d/M0cXLvOFkCuCwcX0DSOhvsukZ1RVK/rHpe9vJgF/KW1cJmM7abvQTA5q7N1WZdwD7tvDF32TTPT2iMK9/28sUDlg8kjxmCt3dkJvBMO+I7mjx7/n4AoaWdIT99Ux2wObOHo4h9XKH8RY6CKzs+gv+JgqDSPl+q3rl4AdhSPZvu5tieUfl+wRQDtOGP5vHYq7qN7q41knvJFAPACXK/m/GlRDzeCB4n3Gocb2Bh9ufbGIhjqM7Fs1cORZOVgAwrhRpCDLGiHG9NlHGgL9L0xgdrBFQ9A4dFAHXUP8aGFxDia+mcTzU7aOwhKSyiT6EZYHKRixSvpfyBSyLRaayMiqcSdfvpS2enkdT1nQser/zkfD4cWxihZTOYh6GujjrLIU6CVdYOhQCvlJXMkR8h84fAr1DqmpcYSOVpSJUW4bWYNmBytIJLy2pLAmPbziqASzrLNWAwXdKbUnrnDj5PgCDG3P8UPdPhccmFpX/8g0QHFX6eRTd6+4fB9CS6uxBKKz8akAfciancxbQRPcGgKZfUn/VN8Co9kSTJ/9+pFOMA1L+e7FNoDFZp5k8mHH82L+3gvx8/tp5cKx1jO3qAjdF97rbHxI+Sr8mivJf6qIPOXopzzJ5PLzksc6tZw70xy9A8fwovtFFDxjSuHhxti7zkjBfbeRnPg0nK5AE2vwX+swS5gROXgZzRiOjxWhb+fc2Fj8p7ykxOpmEm0ThMUeuKxgZ7Og/6p+ZA95d6uyHYDj9BV9DWyThTwDkwoj245iVcZPvABjgYlCJjXX9nedxkvBoWb8icfqBxiNRgzx/wNM5wqODb9Wwtkb50cHFeOrXOpNThCcH/0t1Jzc/Gmzvzr6K4QzhIaIjrbvZBGjl4wtxFF/oOzhDeLSpxg6+UTg5QW6+hJRw5iXKJwg/oBdt62gaJVAViuaLCuBOvHSHX3h0NKJZBD/RKoGqgKnOZoj+tOiGX3jV3NE0tvjibOzkbMJpd+ZmFx5wp9p0jc0I9VIcHWWy4tPTUQNgK1QFP83Ns9/rJYy5Ycr6CGgvfAyHB9ncQXd4c+90twR+uG93gamTrDvHALmxcn+sDwFV21cCojsxumGitKx171pSnVfIrXo88cC8BfPJ2S8PQfichGkhg6OJ1XvFsVVvmXa1fSVA/usXjwDuTvOWlaKacj09aJmbBapoIjMzTzTy6x8mZZaW9RrHY9vaqlqxEkf/KPY/fMMhkHj8MnCN47VwzY4neDR5pAyF5GJgvaEOGXzdr6ZcRwuHpqN05l6eSN7xqeNYhxigwTN4eKSOjzeiZb2qcXzspRz42ljwj5XcliQyR0hz5+ClUC/AwOYpgAe2YQBacCau2FzxGPyNltUKFNg8C83lahKdY+f6cswGuQyepz61pbOAT0DgSKaiUEYIpmGrkc3gQX5yKc5rMBj46VsUx5AnmX1U8imMasTg2Qwe0FbqbFv8+HPoNiRrW6dTYEesTbWwtQYENJ+6P61pfCLkjsGDtP78GVq2tsxBCDyKFM8IfYoRmGh9IuQGNkuLcUxrX4NtK/4NLAP0B76m9e371eyGXMALr5JaijRJHu/nABqCR23jM60zjl9gvIHJrzJKYxteIOnIo4ETHFENNR9ssNWoxoig7sAzxrcb82Qpb9WeY3y8wqaVTR4+5QFbpldmqH2rtlCX013pftKrITF7LneAtO0rmAGBbk3/gmY3R1e+XNBcrmZuDGBEXPeFAbaoZtXXELjZdn6Zw8MPeWT0NGxxPH61fO1riOB/9R1zIXDGNJwWD8s51A0w/huXq+0G7YaxY5JR+EH5vJ6nqnI7iV8KiFan/xcBydfPr+1WD4r+xc5Gs7p4NEu+iAniaLeF/a0nwtHFs14BwvjdYPKqk58Iv/NWxRQa8J57YlRe+R3d5FraD9vYpn0/VwZeF8/YV4Not6ebHOSHA7otxy0khpHXxTPG8XudPEY3n5k8y/j4MGZeF88YTpZIfm+8CIAxzjJq46wVh/D405nG01R4LT6tdNc8oY3OWSySx/XaYxHeZcYuYYTV4rdTqDva+jFprX5MWqf8BeExB6k7wQNnArW3dZ2A+GqQosrrQSmH8Fqwneau8Maq7o2O8uGV8IlOZ6/AITwGNYzhHjvURNU92UEZvln+Yf4MXJW+YPGJOahhhsKa3ZEiTBZfBa/Qmm9YPHUY0LbZAMPpyiDNLgHcAm4Wf8Fp+kP/VPkbPh4zELYRNROs4SQZ6/67oJLwaGVFclosypcvOT+qGSTnAIOymyWc5DqqQNn9t78FQddGXC2eVpDJ46q0cdRwCI+/u+wBCzopQOEvQ3oRTnyOsqvnXR+YXM3N4mnNpsUDVQkJX2bagcJzhvFJJroeHV/qitbQpZf7A/nSuBaLryt2WHxKQMJD4x5KjZlf2QMetHU6BjVdccnCW8I/Wjz+oUqgA3PFx4MNFxcvra8gHzxvp3DKVisvGAMbbKTqvmwyNa5k8NNEf4pFqLXG1YjkZPM7hbAnrna0NLi0LjEg999v+R7HV+VJ+OJq1oQHL7LIra8/03wD4wt0RyX6Jx98xP2p6z2On4MHwXpUY/I47u6K24seM3OPQbnrfZ3n4G3hH5UvJybX43ig/2J7bY9bQcJzykIRg2AdEWtGX/dlE4rj0cfXT06UpY043rQ3+Isac9k4bZ/hSQZl5TRHj9ZP/P7wjvCLgQS6mlWL//wKY8xnfkzSc5NFneGB/ptBUvNdej2V9uwxiS5LOod5sadJaSnV1hZWXVEKP0nGMSNlneFA4tdLWfdlg2RGYWt1PWD9aJa0eYdV4VU9t/sA1uUN3fj1FXs/v/V6pe7KJrFW1zNW1gKv2NzCusWjq1lgtvI62+r1FXs/v/U6zd2XNpnOsU4vs4XnivzB1ia2hK/FHtnc6v+Uut+7dn+7UJV4mYHOqD+ztK4p7Bs4SP1de37eZhm13nU51GKd9qy6Goyd/qfTbHb3NJv9fFqP80vg2mFh1eIp3evwUCVeBhPsDhNV4mVqmc4RyGhXnlXiZbBIh4kq8QvKGZf+PPLcnNaY3u/PI8+i3esH/tmASvTn+8/77OJjix1FOot05TqdTqfT+RqXy39zjOnVHrSANQAAAABJRU5ErkJggg==" alt="" />

Solution for the question - a small body of mass is slides down from the top of a hemisphere of radiusf . the surface of block and hemisphere are frictionless.

A small body of mass is slides down from the top of a hemispher-Turito

Time of flight. <img src="data:image/png;base64,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" class="Wirisformula" alt="T equals fraction numerator 2 u sin invisible function application theta over denominator g end fraction" width="91" height="38" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»T«/mi»«mo»=«/mo»«mfrac»«mrow»«mn»2«/mn»«mi»u«/mi»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»θ«/mi»«/mrow»«/mrow»«/mrow»«mrow»«mi»g«/mi»«/mrow»«/mfrac»«/math»'/> Horizontal range, <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" width="99" 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»«/math»'/> Change in angular momentum, <img src="data:image/png;base64,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" class="Wirisformula" alt="open vertical bar d stack L with rightwards arrow on top close vertical bar equals open vertical bar stack L with rightwards arrow on top subscript f end subscript minus stack L with rightwards arrow on top subscript i end subscript close vertical bar" width="114" height="26" style="vertical-align:-6px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfenced open=¨|¨ close=¨|¨ separators=¨|¨»«mrow»«mi»d«/mi»«mover accent=¨true¨»«mrow»«mi»L«/mi»«/mrow»«mo»→«/mo»«/mover»«/mrow»«/mfenced»«mo»=«/mo»«mfenced open=¨|¨ close=¨|¨ separators=¨|¨»«mrow»«msub»«mrow»«mover accent=¨true¨»«mrow»«mi»L«/mi»«/mrow»«mo»→«/mo»«/mover»«/mrow»«mrow»«mi»f«/mi»«/mrow»«/msub»«mo»-«/mo»«msub»«mrow»«mover accent=¨true¨»«mrow»«mi»L«/mi»«/mrow»«mo»→«/mo»«/mover»«/mrow»«mrow»«mi»i«/mi»«/mrow»«/msub»«/mrow»«/mfenced»«/math»'/> about point of projection <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAK8AAAAqCAYAAADF7wseAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAABFBJREFUeNrtnEFkHFEYx58VURGlKmJVlKiKqgpVUVVRqoeoiFIVPVSEqoocellV1VOJHKqqeumhqocQET1EhIqKiCpRUZVDqOohqkIPURUrbL/PfitjvDfz3uzMZGb2/+PT7Jed1X3vm2++9/3fi1Kg6NTEqmRrZKcwJCBvlMjuk33BUIC8sochAHlkkGwFwwDyRllq3t6IdXMULpHNke1Kzb1BdtvimnmybbnRBjB1rc1psgUJYJVi8HLwjZJ1yuszcgONGt4/IIFbktddZN8xfa2dcRfJjmbk/3OS7Kvhd5yZT/h8S2TnMI3F4glZxcLPgdsX8DlcRnwk+6cO2mphmbfx+qZkxj3Jsj1NLBqvkr3R+GfIhjDdxWKWbMTCX9OYl3WyYceyoSaBOy2ZlBmzXAxelNLBz2uyGxo/lxHXMN3FYkvziA3ym+CMeyxC8F7x+UqyKAviCNlnWZT52TTcaGzdmO7iUJKgs/UHMRKyiAoqG1wWdnyDvDdk0ZJ0JGz9IMcMSJ1q6w+jUx7bm9KZiDt4eyVwTdI0Z9Zljf+CqrfaQIEYNSxu7hj8tjxUevm4meDtkxujI+RmnDcsPsfSHFjWz6daMKCm5LunwXOySU2W+kU23mQ5Uo0xeLtlAdlmkfk3NGUG30jtaU0g9+M+tXBGXFPp9CQ5I72VYOuS1y8lezXTVho3lB1Rg3dBBbfpvHzz3JB9EkfX0568/owGVi2GzwiTLs+TrabwXTgrLUmWXPFM8h9Z0buOC9u+qveEyzEGby3AdIlvQ74TixjDaQZHv9L374oSvLbS5aoEMcgR3LCeKPD3s5UuJ1u05s81PJGXDfVZRYr3F2S/ZWEx5HkEPpNH3q6seP3Xmj7T24pJUuJ0kS5ZQVo2jNEjMdffAccayKVeURJ4upXhrATburR4eOXJkuIPqa84YG6Jv0eCqNtzrY0EmrTE6SJdtqvgxrouSBG4h8y+wb8lmcgvQW5LUOj8Zc+1NhJo0hKnq3QZJpN6gxWBm9HgbciVHY5+/8+m9zRIUuKMIl1WLcaLA/aDQ+DWYIFP/tjLBlcZ0+t3vTYpidNVugwrG6IGL0gQngj/biGTjGnjjyqBxi1xukqXQQs2lA05apVxd+Gu5r02/qgSaNwSp6t0OSFjgQVbjtCJFCa50sYfVQKNW+JkXKTLIJECrbIMw5Pqbdqb5Eobv4sEmqTEqZS9dJmWPAwSABtzcFgw19xTrSmPThvqeAAAAMCdDnmy7Ki6fD8ni+cKhgZkmTZZMFfkZ7YHsjgewfCALPOY7KnGz/tLyhgekGVYFDru83Hv/S+GBmQZU9866hF7AFKD9zC/0/hN+04AyAysJM5o/BzQ4xgekGX4z6Lysa3GiXD+l9tkfGBgEMMD8pB9f6r6vg4+bsXHnnbUwSlqAHLDWUMpAUCm4O2fr9RBP5f3U68p+7+CA8ChwRvx+YAA93T53OCiZN5M8B9WSK8oQ0zFsQAAASt0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+PTwvbW8+PG1vPig8L21vPjxtaT5tPC9taT48bWk+dTwvbWk+PG1pPnNpbjwvbWk+PG1vPiYjeDIwNjE7PC9tbz48bWk+JiN4M0I4OzwvbWk+PG1vPik8L21vPjxtbz4mI3hENzs8L21vPjxtZnJhYz48bXJvdz48bXN1cD48bWk+dTwvbWk+PG1uPjI8L21uPjwvbXN1cD48bWk+c2luPC9taT48bW8+JiN4MjA2MTs8L21vPjxtbj4yPC9tbj48bWk+JiN4M0I4OzwvbWk+PC9tcm93PjxtaT5nPC9taT48L21mcmFjPjwvbWF0aD6El2zSAAAAAElFTkSuQmCC" class="Wirisformula" alt="equals left parenthesis m u sin invisible function application theta right parenthesis cross times fraction numerator u to the power of 2 end exponent sin invisible function application 2 theta over denominator g end fraction" width="175" height="42" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»=«/mo»«mo»(«/mo»«mi»m«/mi»«mi»u«/mi»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»θ«/mi»«/mrow»«/mrow»«mo»)«/mo»«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»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="equals fraction numerator m u to the power of 3 end exponent sin invisible function application theta sin invisible function application 2 theta over denominator g end fraction" width="137" height="42" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»=«/mo»«mfrac»«mrow»«mi»m«/mi»«msup»«mrow»«mi»u«/mi»«/mrow»«mrow»«mn»3«/mn»«/mrow»«/msup»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»θ«/mi»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mn»2«/mn»«mi»θ«/mi»«/mrow»«/mrow»«/mrow»«/mrow»«/mrow»«mrow»«mi»g«/mi»«/mrow»«/mfrac»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="T o r q u e blank open vertical bar stack tau with rightwards arrow on top close vertical bar equals fraction numerator c h a n g e blank i n blank a n g u l a r blank m o m e n t u m over denominator t i m e blank o f blank f l i g h t end fraction" width="344" height="38" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»T«/mi»«mi»o«/mi»«mi»r«/mi»«mi»q«/mi»«mi»u«/mi»«mi»e«/mi»«mi» «/mi»«mfenced open=¨|¨ close=¨|¨ separators=¨|¨»«mrow»«mover accent=¨true¨»«mrow»«mi»τ«/mi»«/mrow»«mo»→«/mo»«/mover»«/mrow»«/mfenced»«mo»=«/mo»«mfrac»«mrow»«mi»c«/mi»«mi»h«/mi»«mi»a«/mi»«mi»n«/mi»«mi»g«/mi»«mi»e«/mi»«mi» «/mi»«mi»i«/mi»«mi»n«/mi»«mi» «/mi»«mi»a«/mi»«mi»n«/mi»«mi»g«/mi»«mi»u«/mi»«mi»l«/mi»«mi»a«/mi»«mi»r«/mi»«mi» «/mi»«mi»m«/mi»«mi»o«/mi»«mi»m«/mi»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»u«/mi»«mi»m«/mi»«/mrow»«mrow»«mi»t«/mi»«mi»i«/mi»«mi»m«/mi»«mi»e«/mi»«mi» «/mi»«mi»o«/mi»«mi»f«/mi»«mi» «/mi»«mi»f«/mi»«mi»l«/mi»«mi»i«/mi»«mi»g«/mi»«mi»h«/mi»«mi»t«/mi»«/mrow»«/mfrac»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="equals open vertical bar fraction numerator d stack L with rightwards arrow on top over denominator T end fraction close vertical bar" width="54" height="43" style="vertical-align:-13px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»=«/mo»«mfenced open=¨|¨ close=¨|¨ separators=¨|¨»«mrow»«mfrac»«mrow»«mi»d«/mi»«mover accent=¨true¨»«mrow»«mi»L«/mi»«/mrow»«mo»→«/mo»«/mover»«/mrow»«mrow»«mi»T«/mi»«/mrow»«/mfrac»«/mrow»«/mfenced»«/math»'/>

Average torque on a projectile 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»'/>, initial speed <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAAKCAYAAABi8KSDAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAG1JREFUeNpjYECAeiAuZ8AEWMVXAXEAFsVYxW8BsTQWxRjiTED8DYtCrOLmQLwfi2Ks4pFAPB+L4nhs4hOAOA9NzBSInwNxMrbgWQh1oyiUPwWI1wGxF7piQSDeAcS/gPggEPtAxd8BMQcDOQAALoQVIlpjITsAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPnU8L21pPjwvbWF0aD6GIoRbAAAAAElFTkSuQmCC" class="Wirisformula" alt="u" width="11" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»u«/mi»«/math»'/> and angles of projection <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»'/>, between initial and final position <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»'/> as shown in figure about the point of projection is <img src="data:image/png;base64,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" alt="" />

Solution for the question - average torque on a projectile of mass is , initial speed u and angles ofprojection theta , between initial and final position p and

Average torque on a projectile of mass is , initial speed u and-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 the string makes <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator 2 over denominator pi end fraction" width="21" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mn»2«/mn»«/mrow»«mrow»«mi»π«/mi»«/mrow»«/mfrac»«/math»'/> rev/s around the vertical axis through, the fixed and as shown in the figure, then tension in the string is <img src="data:image/png;base64,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" alt="" />

Solution for the question - a string of length l is fixed at one end and the string makes (2)/(pi)rev/s around the vertical axis through, the fixed and as shown

A string of length l is fixed at one end and the string makes (-Turito

A thin prism <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAARCAYAAADQWvz5AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAKBJREFUeNpjYMAEP4D4PxR/AeJVQOzIQCJQAeILSHw2IHYB4vtArEWKQQFAvBSLeDIQl5BiUD0ODR1AnEOKQaDw8EMTEwXiW0AsTIpBIA2SSHxjID5KamAzAfEfaGy9gxrQjGYwUcAciPczUAFEAvF8ItSpAXEtWjJBAZOAOI0IgxZD1f3HpWAdEHuR4AOcBoECmIMaBpEKRg3CbwA6ZgAAJNEmhga+DpYAAABgdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1zdWI+PG1pPlA8L21pPjxtbj4xPC9tbj48L21zdWI+PC9tYXRoPkR9VUQAAAAASUVORK5CYII=" class="Wirisformula" alt="P subscript 1 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»P«/mi»«/mrow»«mrow»«mn»1«/mn»«/mrow»«/msub»«/math»'/> with angle <img src="data:image/png;base64,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" class="Wirisformula" alt="6 to the power of ring operator end exponent" width="22" height="16" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msup»«mrow»«mn»6«/mn»«/mrow»«mrow»«mo»∘«/mo»«/mrow»«/msup»«/math»'/> and made from glass of refractive index 1.54 is combined with another thin prism <img src="data:image/png;base64,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" class="Wirisformula" alt="P subscript 2 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»P«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msub»«/math»'/> of refractive index 1.72 to produce dispersion without deviation. The angle of prism <img src="data:image/png;base64,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" class="Wirisformula" alt="P subscript 2 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»P«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msub»«/math»'/> will be

Solution for the question - a thin prism p_(1) with angle 6^(@) and made from glass of refractive index1.54 is combined with another thin prism p_(2) of refract

A thin prism p_(1) with angle 6^(@) and made from glass of refr-Turito

For total internal reflection <img src="data:image/png;base64,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" class="Wirisformula" alt="theta greater than C" width="39" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»θ«/mi»«mo»§gt;«/mo»«mi»C«/mi»«/math»'/> <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAKCAYAAAC0VX7mAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAADlJREFUeNpjYCANlAAxHwMVQTUQPwRia1I0/ScStwIxE7VcOhdq6FJqurCDGi4kKwwJxTIPwyhABgA3dxtvdcXJJQAAAFB0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4MjFEMjs8L21vPjwvbWF0aD5WOBRoAAAAAElFTkSuQmCC" class="Wirisformula" alt="rightwards double arrow" width="20" height="10" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»⇒«/mo»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="sin invisible function application theta greater than sin invisible function application C rightwards double arrow sin invisible function application theta greater than fraction numerator 1 over denominator mu end fraction" width="174" height="38" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»θ«/mi»«/mrow»«/mrow»«mo»§gt;«/mo»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»C«/mi»«/mrow»«/mrow»«mo»⇒«/mo»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»θ«/mi»«/mrow»«/mrow»«mo»§gt;«/mo»«mfrac»«mrow»«mn»1«/mn»«/mrow»«mrow»«mi»μ«/mi»«/mrow»«/mfrac»«/math»'/> or <img src="data:image/png;base64,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" class="Wirisformula" alt="mu greater than fraction numerator 1 over denominator sin invisible function application theta end fraction rightwards double arrow mu greater than fraction numerator 1 over denominator sin invisible function application 4 5 to the power of o end exponent end fraction rightwards double arrow mu greater than square root of 2 rightwards double arrow mu greater than 1.41" width="328" height="38" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»μ«/mi»«mo»§gt;«/mo»«mfrac»«mrow»«mn»1«/mn»«/mrow»«mrow»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»θ«/mi»«/mrow»«/mrow»«/mrow»«/mfrac»«mo»⇒«/mo»«mi»μ«/mi»«mo»§gt;«/mo»«mfrac»«mrow»«mn»1«/mn»«/mrow»«mrow»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mn»4«/mn»«/mrow»«/mrow»«msup»«mrow»«mn»5«/mn»«/mrow»«mrow»«mi»o«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«mo»⇒«/mo»«mi»μ«/mi»«mo»§gt;«/mo»«msqrt»«mn»2«/mn»«/msqrt»«mo»⇒«/mo»«mi»μ«/mi»«mo»§gt;«/mo»«mn»1.41«/mn»«/math»'/>

A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if <img src="data:image/png;base64,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" class="Wirisformula" alt="theta equals 4 5 to the power of o end exponent" width="56" height="15" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»θ«/mi»«mo»=«/mo»«mn»4«/mn»«msup»«mrow»«mn»5«/mn»«/mrow»«mrow»«mi»o«/mi»«/mrow»«/msup»«/math»'/>. The index of refraction of glass is <img src="data:image/png;base64,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" alt="" />

Solution for the question - a triangular prism of glass is shown in the figure. a ray incident normallyto one face is totally reflected, if theta=45^(@) . the i