A solid sphere rolls without slipping on an i | vedclass

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

Question

(B) For a solid sphere, the moment of inertia about its center of mass is $I = \frac{2}{5}MR^2$.Since the sphere rolls without slipping, its linear ve

Vedclass · Accepted Answer

$7/2$

Vedclass · Answer

(B) For a solid sphere, the moment of inertia about its center of mass is $I = \frac{2}{5}MR^2$.Since the sphere rolls without slipping, its linear velocity $v$ and angular velocity $\omega$ are related by $v = R\omega$.The rotational kinetic energy is $K_{rot} = \frac{1}{2}I\omega^2 = \frac{1}{2}(\frac{2}{5}MR^2)(\frac{v^2}{R^2}) = \frac{1}{5}Mv^2$.The translational kinetic energy is $K_{trans} = \frac{1}{2}Mv^2$.The total kinetic energy is $K_{total} = K_{trans} + K_{rot} = \frac{1}{2}Mv^2 + \frac{1}{5}Mv^2 = \frac{7}{10}Mv^2$.The ratio of total kinetic energy to rotational kinetic energy is $\frac{K_{total}}{K_{rot}} = \frac{\frac{7}{10}Mv^2}{\frac{1}{5}Mv^2} = \frac{7}{10} 	imes 5 = \frac{7}{2}$.

$A$ solid sphere rolls without slipping on an inclined plane at an angle $\theta$. The ratio of total kinetic energy to its rotational kinetic energy is

Similar Questions

$A$ disc of mass $M$ and radius $R$ rolls on a horizontal surface and then rolls up an inclined plane as shown in the figure. If the velocity of the disc is $v,$ the height to which the disc will rise will be

$A$ cylinder rolls up an inclined plane to a certain height and then rolls down. (During these motions,the cylinder rolls without slipping). What are the directions of the frictional force acting on the cylinder?

If a sphere is rolling,the ratio of its rotational energy to the total kinetic energy is given by

$A$ sphere is rolling down an incline without slipping. If the height of the incline is $14 \ m$,find its linear velocity at the bottom.

$A$ body starts rolling down an inclined plane of length $L$ and height $h$. This body reaches the bottom of the plane in time $t$. The relation between $L$ and $t$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module