Question

A rigid body rotates with an angular momentum $L$ . If its rotational kinetic energy is made 4 times, its momentum will become

• A. 4 $L$
• B. 16 $L$
• C. $\sqrt{2}$ $L$
• D. 2$L$

Answer 1

The correct option is D 2$L$

we know that $L=I\omega K.E=K=\frac{1}{2}I{\omega }^2{L}^2=I^2{\omega }^{2}thenk=\frac{L^2}{2I}$
$L=\sqrt{2KI},\frac{L_1}{L_2}=\sqrt{\frac{K_1}{K_2}}L\propto \sqrt{K},L_f=2L$