(C) Using the principle of conservation of mechanical energy,the loss in potential energy of the block is equal to the gain in kinetic energy of the s

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(C) Using the principle of conservation of mechanical energy,the loss in potential energy of the block is equal to the gain in kinetic energy of the system (block + disc).Loss in potential energy of the block = $m g h$Gain in kinetic energy of the block = $\frac{1}{2} m v^2$Gain in rotational kinetic energy of the disc = $\frac{1}{2} I \omega^2 = \frac{1}{2} (\frac{1}{2} m r^2) (\frac{v}{r})^2 = \frac{1}{4} m v^2$Equating the energies: $m g h = \frac{1}{2} m v^2 + \frac{1}{4} m v^2$$m g h = \frac{3}{4} m v^2$$v^2 = \frac{4 g h}{3}$$v = \sqrt{\frac{4 g h}{3}} = 2 \sqrt{\frac{g h}{3}}$

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

Medium

$A$ disc of mass $m$ and radius $r$ is free to rotate about its centre as shown in the figure. $A$ string is wrapped over its rim and a block of mass $m$ is attached to the free end of the string. The system is released from rest. The speed of the block as it descends through a height $h$ is:

A
$\sqrt{2 g h}$
B
$\sqrt{\frac{2}{3} g h}$
C
$2 \sqrt{\frac{g h}{3}}$
D
$\frac{1}{2} \sqrt{3 g h}$

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System of Particles and Rotational Motion

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Rotation Motion Basic, Motion of Connected Mass

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In the given figure,a solid cylinder of mass $m_2$ and radius $R$ is suspended by a string wrapped around it,which passes over a fixed pulley of mass $m_1$ and radius $R$. If the linear acceleration of the solid cylinder is $a_2$ and there is no slipping,what is its angular acceleration $\alpha_2$?

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$A$ disc of mass $m$ and radius $r$ is free to rotate about its centre as shown in the figure. $A$ string is wrapped over its rim and a block of mass $m$ is attached to the free end of the string. The system is released from rest. The speed of the block as it descends through a height $h$ is:

Similar Questions

When a ceiling fan is switched off,its angular velocity falls to $\frac{1}{3}$ of its initial value while it makes $24$ rotations. How many more rotations will it make before coming to rest?

In the given figure,the linear acceleration of the solid cylinder of mass $m_2$ is $a_2$. If there is no slipping,find its angular acceleration $\alpha_2$.

$A$ rigid body rotates about a fixed axis with variable angular velocity equal to $\alpha - \beta t$,where $t$ is time and $\alpha, \beta$ are constants. Find the angle (in radians) through which it rotates before it stops.

In the given figure,a solid cylinder of mass $m_2$ and radius $R$ is suspended by a string wrapped around it,which passes over a fixed pulley of mass $m_1$ and radius $R$. If the linear acceleration of the solid cylinder is $a_2$ and there is no slipping,what is its angular acceleration $\alpha_2$?

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