In the figure,E and v_{cm} represent the tota | vedclass

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

Question

(C) The total kinetic energy of an object in pure rolling motion is given by:$E = \frac{1}{2} m v_{cm}^{2} \left(1 + \frac{k^{2}}{R^{2}}\right)$where

Vedclass · Accepted Answer

disc

Vedclass · Answer

(C) The total kinetic energy of an object in pure rolling motion is given by:$E = \frac{1}{2} m v_{cm}^{2} \left(1 + \frac{k^{2}}{R^{2}}\right)$where $k$ is the radius of gyration,$R$ is the radius,and $m$ is the mass of the object.Given $m = 1 \ kg$,the expression becomes:$\frac{E}{v_{cm}^{2}} = \frac{1}{2} \left(1 + \frac{k^{2}}{R^{2}}\right) \quad ...(i)$From the given graph,the slope of the line is $\frac{E}{v_{cm}^{2}} = \frac{3}{4}$.Substituting this value into Eq. $(i)$:$\frac{3}{4} = \frac{1}{2} \left(1 + \frac{k^{2}}{R^{2}}\right)$$\frac{3}{2} = 1 + \frac{k^{2}}{R^{2}}$$\frac{k^{2}}{R^{2}} = \frac{3}{2} - 1 = \frac{1}{2}$We know that for a disc,the moment of inertia $I = \frac{1}{2} m R^{2}$,so $k^{2} = \frac{1}{2} R^{2}$,which means $\frac{k^{2}}{R^{2}} = \frac{1}{2}$.Thus,the object is a disc.

In the figure,$E$ and $v_{cm}$ represent the total energy and speed of the centre of mass of an object of mass $1 \ kg$ in pure rolling. The object is

Similar Questions

$A$ solid sphere of mass $5 \,kg$ rolls on a plane surface. Find its kinetic energy at an instant when its centre moves with speed $4 \,m/s$. (in $\,J$)

Why are the contact points of the surface of a circular body stationary during pure rolling motion?

Three solid spheres are made to move on a rough horizontal surface. Sphere $P$ is given a spin and released. Sphere $Q$ is given a forward linear velocity. Sphere $R$ is given linear and rotational motions as shown in the figure. Directions of the friction force on spheres $P, Q, R$ are respectively

$A$ wheel of radius $1 \ m$ rolls through $180^{\circ}$ over a plane surface. The magnitude of the displacement of the point of the wheel initially in contact with the surface is:

$A$ wheel is rolling on the ground with a speed of $2 \ m/s$. What is the velocity of the endpoints of the horizontal diameter of the wheel?

Vedclass Test Series

Exam Paper Generator

Online Exam Module