Physics-
General
Easy
Question
A particle of mass
is rotating in a horizontal circle of radius
and is attached to a hanging mass
as shown in the figure. The speed of rotation required by the mass
keep
steady is
![](data:image/png;base64,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)
The correct answer is: ![square root of fraction numerator m g R over denominator m end fraction end root](data:image/png;base64,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)
To keep the mass M steady, let T is the tension in the string joining the two. Then for particle ![m comma](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABUAAAAMCAYAAACNzvbFAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAKlJREFUeNpjYECAeiAuB2JxIJ4ExC+B+DkQe0HlBYG4D4jfAfEnIK5kIAKsghp8BogjgZgFiOWB+D4QSwLxQSAOh4rLAvEPqAPwgltAvBfqImTwFIhn4xCXxGcgExB/A2IuEsXxAnMg3k8FcRQACsP5VBBHAaDYTqOCOApYh5R0yBFfDsT/gTgAWREo7XFg0UysOFZDqQGW4/AV2cAAiK9AMwbVgDRy7gIAWjAoKUeM/uYAAABTdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPm08L21pPjxtbz4sPC9tbz48L21hdGg+yOpfKQAAAABJRU5ErkJggg==)
![T equals fraction numerator m v to the power of 2 end exponent over denominator R end fraction open parentheses i close parentheses](data:image/png;base64,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)
For mass ![M comma](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAPCAYAAADkmO9VAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAOFJREFUeNpjYEAFP4DYhQE/AMn/AWImAuoYVID4PxBPwaOGB4gfAvElBiJAABBfAOLneNTMhKpZToyB9UBcDsQ3gNgch1dBLmuEqiMIVkFd2QrFyIALiG8BsQGSOoIApEEa6robaHKTkCy5AVWHF4Bi7BsSHxSOGlC2NRBfAWIWLOpwApCr9qMFfjmSV41xqMMJIoF4PloEnATiCWjhia4OJwCFURpaEHwC4mtQr+JShxOsA2IvNLHFSF7Fp245NEOgxPw7IOYgwmJs6rAaSClYjsXlZAMDpGRFFQBK5OIwDgBmXDD9iII/nQAAAFN0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+TTwvbWk+PG1vPiw8L21vPjwvbWF0aD7KD1OxAAAAAElFTkSuQmCC)
![T equals M g left parenthesis i i right parenthesis](data:image/png;base64,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)
From Eqs. (i) and (ii)
![fraction numerator m v to the power of 2 end exponent over denominator R end fraction equals M g ⟹ v equals square root of fraction numerator M g R over denominator m end fraction end root](data:image/png;base64,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)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/487048/1/937241/Picture660.png)
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![](data:image/png;base64,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)
From an inclined plane two particles are projected with same speed at same angle
, one up and other down the plane as shown in figure. Which of the following statements
is/are correct?
![](data:image/png;base64,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)
physics-General
Physics-
Two particles 1 and 2 are projected with same speed
as shown in figure. Particle 2 is on the ground and particle 1 is at a height
from the ground and at a horizontal distance
from particle 2. If a graph is plotted between
and
for the condition of collision of the two then (
on
-axis and
on
-axis
![](data:image/png;base64,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)
Two particles 1 and 2 are projected with same speed
as shown in figure. Particle 2 is on the ground and particle 1 is at a height
from the ground and at a horizontal distance
from particle 2. If a graph is plotted between
and
for the condition of collision of the two then (
on
-axis and
on
-axis
![](data:image/png;base64,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)
Physics-General
physics-
a) Name the experiment for which the adjacent graph, showing the variation of intensity of scattered electrons with the angle of scatter ing (q) was obtained.
b) Also name the important hypothesis that was confirmed by this experiment
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/458425/1/937176/Picture64.png)
a) Name the experiment for which the adjacent graph, showing the variation of intensity of scattered electrons with the angle of scatter ing (q) was obtained.
b) Also name the important hypothesis that was confirmed by this experiment
![](https://mycourses.turito.com/pluginfile.php/1/question/questiontext/458425/1/937176/Picture64.png)
physics-General
physics-
Three identical particles are joined together by a thread as shown in figure. All the three particles are moving in a horizontal plane. If the velocity of the outermost particle is
, then the ratio of tensions in the three sections of the string is
![](data:image/png;base64,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)
Three identical particles are joined together by a thread as shown in figure. All the three particles are moving in a horizontal plane. If the velocity of the outermost particle is
, then the ratio of tensions in the three sections of the string is
![](data:image/png;base64,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)
physics-General
physics-
A ball of mass
kg is attached to the end of a string having length
0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in rad/s) is
![](data:image/png;base64,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)
A ball of mass
kg is attached to the end of a string having length
0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in rad/s) is
![](data:image/png;base64,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)
physics-General
maths-
The ellipse
and the straight line y = mx + c intersect in real points only if
The ellipse
and the straight line y = mx + c intersect in real points only if
maths-General
Physics-
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
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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
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Physics-General
physics-
Four capacitors are connected as shown in figure. The equivalent capacitance between
and
is
![](data:image/png;base64,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)
Four capacitors are connected as shown in figure. The equivalent capacitance between
and
is
![](data:image/png;base64,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)
physics-General
physics-
A frictionless track
ends in a circular loop of radius
figure. A body slides down the track from point
which is at a height
cm. Maximum value of
for the body to successfully complete the loop is
![](data:image/png;base64,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)
A frictionless track
ends in a circular loop of radius
figure. A body slides down the track from point
which is at a height
cm. Maximum value of
for the body to successfully complete the loop is
![](data:image/png;base64,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)
physics-General
physics-
In a circuit shown in figure, the potential difference across the capacitor of 2 F is
![](data:image/png;base64,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)
In a circuit shown in figure, the potential difference across the capacitor of 2 F is
![](data:image/png;base64,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)
physics-General
physics-
The effective capacitance between points
and
shown in figure. Assuming
F and that outer capacitors are all
F is
![](data:image/png;base64,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)
The effective capacitance between points
and
shown in figure. Assuming
F and that outer capacitors are all
F is
![](data:image/png;base64,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)
physics-General