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(D) The rotational kinetic energy $K$ of a rigid body is related to its angular momentum $L$ and moment of inertia $I$ by the formula: $K = \frac{L^2}

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$2 \,L$

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(D) The rotational kinetic energy $K$ of a rigid body is related to its angular momentum $L$ and moment of inertia $I$ by the formula: $K = \frac{L^2}{2I}$.From this, we can express angular momentum as $L = \sqrt{2KI}$.Let the initial kinetic energy be $K_1 = K$ and the initial angular momentum be $L_1 = L$.If the kinetic energy is made four times, the new kinetic energy is $K_2 = 4K$.The new angular momentum $L_2$ will be:$L_2 = \sqrt{2 K_2 I} = \sqrt{2(4K)I} = \sqrt{4(2KI)} = 2\sqrt{2KI}$.Since $L = \sqrt{2KI}$, we have $L_2 = 2L$.

$A$ rigid body rotates with an angular momentum $L$. If its rotational kinetic energy is made four times, its angular momentum will become

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