(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

$A$ thin ring of radius $R$ is rotated about its center. Then its radius:

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$A$ disc rotating about its axis from rest,acquires the angular speed $100 \, rev/s$ in $4 \, s$. The angle rotated by it during these four seconds (in radian) is ...... $\pi$.

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Two masses $400 \ g$ and $350 \ g$ are suspended from the ends of a light string passing over a heavy pulley of radius $2 \ cm$. When released from rest, the heavier mass is observed to fall $81 \ cm$ in $9 \ s$. The rotational inertia of the pulley is . . . . . . $kg \cdot m^2$. $(g = 9.8 \ m/s^2)$

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$A$ string is wrapped around a disc of mass $M$ and radius $R$ and the free end is fixed to the ceiling. The centre of mass falls down as the disc unwinds the string. The tension in the string is

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$A$ cylinder of mass $M$ and radius $r$ is mounted on a frictionless axle over a well. $A$ rope of negligible mass is wrapped around the cylinder and a bucket of mass $m$ is suspended from the rope. The linear acceleration of the bucket will be

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$A$ thin ring of radius $R$ is rotated about its center. Then its radius:

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