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  4. A tennis ball (treated as hollow spherical shell) starting from O rolls down a hill. At point A the ball becomes air borne leaving at an angle of 30° with the horizontal. The ball strikes the ground at B. What is the value of the distance AB ? (Moment of inertia of a spherical shell of mass m and radius R about its diameter =(2/3)mR2 )

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Q. A tennis ball (treated as hollow spherical shell) starting from $O$ rolls down a hill. At point A the ball becomes air borne leaving at an angle of $30^\circ$ with the horizontal. The ball strikes the ground at $B$. What is the value of the distance $AB$ ?
(Moment of inertia of a spherical shell of mass $m$ and radius $R$ about its diameter $=\frac{2}{3}mR^{2}$ )Physics Question Image

JEE MainJEE Main 2013System of Particles and Rotational Motion

Solution:

Velocity of the tennis ball on the surface of the earth or ground
$v=\sqrt{\frac{2gh}{1+\frac{k^{2}}{R^{2}}}}$ ( where k = radius of gyration of spherical shell $=\sqrt{\frac{2}{3}R}$ )
Horizontal range $AB=\frac{v^{2}\,sin\,2\theta}{g}$
$=\frac{\left(\frac{\sqrt{ 2gh}}{1+k^{2}/R^{2}}\right)sin\left(2\times30^{°}\right)}{g}$