JEE Main · PhysicsMedium

$A solid sphere of mass $M$ and radius $R$ rolls without slipping on a horizontal surface with a linear velocity $v$. What is the total kinetic energy of the sphere?$

Show correct answer & step-by-step solution

Correct answer: B — $$0.7 M v^2$$

Solution

The total kinetic energy is

K = K_{trans} + K_{rot} = \frac{1}{2} M v^{2} + \frac{1}{2} I ω^{2}

. Substituting

I = \frac{2}{5} M R^{2}

and

ω = \frac{v}{R}

, we get

K = \frac{1}{2} M v^{2} + \frac{1}{5} M v^{2} = 0.7 M v^{2}