(C) The velocity of each ball just before hitting the ground is $v = \sqrt{2gh} = \sqrt{2 \times 10 \times 5} = 10 \ m/s$.After the collision,the rebo

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(C) The velocity of each ball just before hitting the ground is $v = \sqrt{2gh} = \sqrt{2 \times 10 \times 5} = 10 \ m/s$.After the collision,the rebound velocities of the balls are:$v_A = e_A v = 0.6 \times 10 = 6 \ m/s$ (upwards)$v_B = e_B v = 0.4 \times 10 = 4 \ m/s$ (upwards)Since the rod is rigid,the angular velocity $\omega$ of the rod about its center of mass (or relative to the rod's rotation) is given by the difference in velocities divided by the length of the rod:$\omega = \frac{v_A - v_B}{L} = \frac{6 - 4}{0.4} = \frac{2}{0.4} = 5 \ rad/s$.

Class 11 Physics System of Particles and Rotational Motion Rotation Motion Basic, Motion of Connected Mass

Difficult

Two small balls are fixed at the ends of a light rigid rod of length $L = 0.4 \ m$. The system is released from a height $h = 5 \ m$ with the rod horizontal. The balls collide with the horizontal surface and rebound. The coefficient of restitution between ball $A$ and the ground is $e_A = 0.6$ and that between ball $B$ and the ground is $e_B = 0.4$. Find the angular speed (in $rad/s$) of the rod just after the collision. Take the acceleration due to gravity $g = 10 \ m/s^2$.

A
$0$
B
$2.5$
C
$5$
D
$9$

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System of Particles and Rotational Motion

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Rotation Motion Basic, Motion of Connected Mass

One end of a rod of length $L$ is on a horizontal plane. It is inclined at an angle $\alpha$ to the horizontal plane. When released,its angular velocity after coming to the horizontal plane is:

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The pulley shown in the figure is made using a thin rim and two rods of length equal to the diameter of the rim. The rim and each rod have a mass of $M$. Two blocks of mass $M$ and $m$ are attached to two ends of a light string passing over the pulley, which is hinged to rotate freely in a vertical plane about its centre. The magnitude of the acceleration experienced by the blocks is . . . . . . (assume no slipping of the string on the pulley.)

DifficultJEE MAIN 2026

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For the given figure,find the acceleration of the $1\, kg$ block. The string is massless,the mass of the pulley is $M = 2\, kg$,and the diameter of the pulley is $0.2\, m$. (in $m/s^2$)

DifficultAIIMS 2019

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In the motion of a spinning top at any one place,does the point in the spinning top remain stationary or does the line remain stationary?

Medium

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$A$ mass $m$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R$. If the string does not slip on the cylinder,with what acceleration will the mass fall on release?

MediumJEE MAIN 2014

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One end of a rod of length $L$ is on a horizontal plane. It is inclined at an angle $\alpha$ to the horizontal plane. When released,its angular velocity after coming to the horizontal plane is:

For the given figure,find the acceleration of the $1\, kg$ block. The string is massless,the mass of the pulley is $M = 2\, kg$,and the diameter of the pulley is $0.2\, m$. (in $m/s^2$)

In the motion of a spinning top at any one place,does the point in the spinning top remain stationary or does the line remain stationary?

$A$ mass $m$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R$. If the string does not slip on the cylinder,with what acceleration will the mass fall on release?

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