Question

A hollow sphere of mass $m$ starting from rest rolls down, without slipping, on an inclined plane of inclination $\theta$. What is the total energy of the sphere after ${10}^{-5}s$ if velocity after ${10}^{-5}s$ is $v$?

• A. $5/6m{v}^2$
• B. $2/3m{v}^2$
• C. ${10}^{-5}m{v}^2$
• D. $m{v}^2/{10}^{-5}$

Answer 1

The correct option is A $5/6m{v}^2$

Total K.E, $E=\frac{1}{2}m{v}^2+\frac{1}{2}I{w}^2$

$E=\frac{1}{2}m{v}^2+\frac{1}{2}\times \frac{2}{3}m{R}^2{w}^2$

$E=\frac{1}{2}m{v}^2+\frac{1}{2}\times \frac{2}{3}m{v}^2$ (as $v=Rw$ no slipping)

$E=\frac{5}{6}m{v}^2$