A disc and a ring of same mass are rolling an | vedclass

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

Question

${K_{disc}} = \frac{1}{2}mv_d^2\left( {1 + \frac{{{k^2}}}{{{R^2}}}} \right)\,$$ = \frac{3}{4}mv_d^2$  $\left[ {As\frac{{{k^2}}}{{{R^2}}} = \frac{

Vedclass · Accepted Answer

$\sqrt 4 :\sqrt 3 $

Vedclass · Answer

${K_{disc}} = \frac{1}{2}mv_d^2\left( {1 + \frac{{{k^2}}}{{{R^2}}}} \right)\,$$ = \frac{3}{4}mv_d^2$  $\left[ {As\frac{{{k^2}}}{{{R^2}}} = \frac{1}{2}\,\,\,\,\,\,{\rm{for disc}}} \right]$

${K_{ring}} = \frac{1}{2}m{v_r}\left( {1 + \frac{{{k^2}}}{{{R^2}}}} \right)$$ = mv_r^2$               $\left[ {As\frac{{{k^2}}}{{{R^2}}} = 1\,\,\,\,\,\,\,{\rm{for ring}}} \right]$

According to problem ${K_{disc}} = {K_{ring}}$

$\frac{3}{4}mv_d^2 = mv_r^2$ 

$\frac{{{v_d}}}{{{v_r}}} = \sqrt {\frac{4}{3}} $.

A disc and a ring of same mass are rolling and if their kinetic energies are equal, then the ratio of their velocities will be

Similar Questions

A body of moment of inertia of $3\ kg-m^2$ rotating with an angular velocity of $2\ rad/sec$ has the same kinetic energy as a mass of $12\ kg$ moving with a velocity of .......... $m/s$

The ratio of rotational and translatory kinetic energies of a sphere is

$A$ rod is hinged at its centre and rotated by applying a constant torque starting from rest. The power developed by the external torque as a function of time is :

The angular velocity of a body is $\mathop \omega \limits^ \to = 2\hat i + 3\hat j + 4\hat k$ and a torque $\mathop \tau \limits^ \to = \hat i + 2\hat j + 3\hat k$ acts on it. The rotational power will be .......... $W$

A disc is rotating with angular velocity $\vec{\omega}$. A force $\vec{F}$ acts at a point whose position vector with respect to the axis of rotation is $\vec{r}$. The power associated with torque due to the force is given by ..........