A massless string is wrapped around a disc of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) According to the law of conservation of energy,the potential energy lost by the mass $m$ is converted into the kinetic energy of the mass $m$ and

Vedclass · Accepted Answer

$\sqrt{\frac{4mgh}{2m + M}}$

Vedclass · Answer

(D) According to the law of conservation of energy,the potential energy lost by the mass $m$ is converted into the kinetic energy of the mass $m$ and the rotational kinetic energy of the disc.$mgh = \frac{1}{2} mv^{2} + \frac{1}{2} I\omega^{2}$Since the string is wrapped around the disc,the moment of inertia of the disc is $I = \frac{1}{2} MR^{2}$ and the angular velocity is $\omega = \frac{v}{R}$.Substituting these values:$mgh = \frac{1}{2} mv^{2} + \frac{1}{2} \left( \frac{1}{2} MR^{2} \right) \left( \frac{v}{R} \right)^{2}$$mgh = \frac{1}{2} mv^{2} + \frac{1}{4} Mv^{2}$$mgh = v^{2} \left( \frac{2m + M}{4} \right)$$v^{2} = \frac{4mgh}{2m + M}$$v = \sqrt{\frac{4mgh}{2m + M}}$

$A$ massless string is wrapped around a disc of mass $M$ and radius $R$. Another end is tied to a mass $m$ which is initially at height $h$ from the ground level as shown in the figure. If the mass is released,then its velocity while touching the ground level will be:

Similar Questions

$A$ rod of length $1 \ m$ is held vertically. What will be the speed of the other end when it touches the ground without slipping?

If $\vec{\omega} = (3\hat{i} + 4\hat{j} + 5\hat{k}) \text{ rad/s}$ and $\vec{r} = (\hat{i} - 2\hat{j} + 3\hat{k}) \text{ m}$,then the linear velocity vector of the particle is:

The variation of angular position $\theta$ of a point on a rotating rigid body with time $t$ is shown in the figure. Is the body rotating clockwise or anti-clockwise?

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:

Vedclass Test Series

Exam Paper Generator

Online Exam Module