A solid sphere rolls down without slipping on | 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 $I = \frac{2}{5} MR^2$.Since the sphere rolls without slipping,the condition $V = \omega R$ holds,which i

Vedclass · Accepted Answer

$28.6$

Vedclass · Answer

(B) For a solid sphere,the moment of inertia $I = \frac{2}{5} MR^2$.Since the sphere rolls without slipping,the condition $V = \omega R$ holds,which implies $\omega = \frac{V}{R}$.The rotational kinetic energy is $E_r = \frac{1}{2} I \omega^2 = \frac{1}{2} (\frac{2}{5} MR^2) (\frac{V}{R})^2 = \frac{1}{5} MV^2$.The translational kinetic energy is $E_t = \frac{1}{2} MV^2$.The total kinetic energy is $E_{total} = E_r + E_t = \frac{1}{5} MV^2 + \frac{1}{2} MV^2 = \frac{7}{10} MV^2$.The ratio of rotational kinetic energy to total energy is $\frac{E_r}{E_{total}} = \frac{\frac{1}{5} MV^2}{\frac{7}{10} MV^2} = \frac{1}{5} 	imes \frac{10}{7} = \frac{2}{7}$.To find the percentage,we calculate $\frac{2}{7} 	imes 100 \approx 28.57\%$,which rounds to $28.6\%$.

$A$ solid sphere rolls down without slipping on an inclined plane,then the percentage of rotational kinetic energy of the total energy will be ........ $\%.$

Similar Questions

$A$ solid sphere rolls without slipping,first horizontally and then up to a point $X$ at height $h$ on an inclined plane before rolling down,as shown in the figure below. The initial horizontal speed of the sphere is

$A$ solid cylinder of mass $m$ and radius $R$ rolls down an inclined plane of height $h$ without slipping. The speed of its centre of mass when it reaches the bottom is

An inclined plane makes an angle $30^{\circ}$ with the horizontal. $A$ solid sphere rolling down an inclined plane from rest without slipping has a linear acceleration (where $g$ is the acceleration due to gravity and $\sin 30^{\circ} = 0.5$).

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

$A$ cylinder rolls up an inclined plane to a certain height and then rolls down. (It does not slip during the entire motion.) What is the direction of the frictional force acting on the cylinder?

Vedclass Test Series

Exam Paper Generator

Online Exam Module