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(D) The rotational kinetic energy $(K.E._{rot})$ is given by the formula: $K.E._{rot} = \frac{1}{2} I \omega^2$.For a solid sphere,the moment of inert

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$45$

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(D) The rotational kinetic energy $(K.E._{rot})$ is given by the formula: $K.E._{rot} = \frac{1}{2} I \omega^2$.For a solid sphere,the moment of inertia $(I)$ about an axis passing through its centre is $I = \frac{2}{5} MR^2$.Given: Mass $(M)$ = $1\,kg$,Radius $(R)$ = $30\,cm = 0.3\,m$,Angular velocity $(\omega)$ = $50\,rad/s$.Substituting the values into the formula:$I = \frac{2}{5} 	imes 1 	imes (0.3)^2 = 0.4 	imes 0.09 = 0.036\,kg \cdot m^2$.$K.E._{rot} = \frac{1}{2} 	imes 0.036 	imes (50)^2$.$K.E._{rot} = 0.5 	imes 0.036 	imes 2500$.$K.E._{rot} = 0.018 	imes 2500 = 45\,J$.

$A$ spherical solid ball of $1\,kg$ mass and radius $30\,cm$ is rotating about an axis passing through its centre with an angular velocity of $50\,rad/s$. The kinetic energy of rotation is ......... $J$.

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