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 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
$\frac{1}{2} \sqrt{3 g h}$
Similar Questions
Write the formula for rotational kinetic energy.
Write the formula for rotational kinetic energy.
A rolling wheel of $12 \,kg$ is on an inclined plane at position $P$ and connected to a mass of $3 \,kg$ through a string of fixed length and pulley as shown in figure. Consider $PR$ as friction free surface. The velocity of centre of mass of the wheel when it reaches at the bottom $Q$ of the inclined plane $P Q$ will be $\frac{1}{2} \sqrt{ xgh } \,m / s$. The value of $x$ is.............
A rolling wheel of $12 \,kg$ is on an inclined plane at position $P$ and connected to a mass of $3 \,kg$ through a string of fixed length and pulley as shown in figure. Consider $PR$ as friction free surface. The velocity of centre of mass of the wheel when it reaches at the bottom $Q$ of the inclined plane $P Q$ will be $\frac{1}{2} \sqrt{ xgh } \,m / s$. The value of $x$ is.............
- [JEE MAIN 2022]
Two rotating bodies $A$ and $B$ of masses $m$ and $2\,m$ with moments of inertia $I_A$ and $I_B (I_B> I_A)$ have equal kinetic energy of rotation. If $L_A$ and $L_B$ be their angular momenta respectively, then
Two rotating bodies $A$ and $B$ of masses $m$ and $2\,m$ with moments of inertia $I_A$ and $I_B (I_B> I_A)$ have equal kinetic energy of rotation. If $L_A$ and $L_B$ be their angular momenta respectively, then
- [NEET 2016]
A flywheel is making $\frac{3000}{\pi}$ revolutions per minute about its axis. If the moment of inertia of the flywheel about that axis is $400\, kgm^2$, its rotational kinetic energy is
A flywheel is making $\frac{3000}{\pi}$ revolutions per minute about its axis. If the moment of inertia of the flywheel about that axis is $400\, kgm^2$, its rotational kinetic energy is
This question has Statement $1$ and Statement $2$. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement $1$ : When moment of inertia $I$ of a body rotating about an axis with angular speed $\omega $ increases, its angular momentum $L$ is unchanged but the kinetic energy $K$ increases if there is no torque applied on it.
Statement $2$ : $L = I\omega $, kinetic energy of rotation $ = \frac{1}{2}\,I\omega ^2$
This question has Statement $1$ and Statement $2$. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement $1$ : When moment of inertia $I$ of a body rotating about an axis with angular speed $\omega $ increases, its angular momentum $L$ is unchanged but the kinetic energy $K$ increases if there is no torque applied on it.
Statement $2$ : $L = I\omega $, kinetic energy of rotation $ = \frac{1}{2}\,I\omega ^2$
- [AIEEE 2012]