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Question

Physics Question on torque

Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio

A

1:02

B

2:1\sqrt{2}:1

C

2:01

D

1:2\sqrt{2}

Answer

1:2\sqrt{2}

Explanation

Solution

Rotational kinetic energy remains same i,e;12I1ω12=12I2ω22i,e; \frac{1}{2}I_1 \omega^2_1=\frac{1}{2}I_2 \omega^2_2 or 12I1(I1ω1)2=12I2(I2ω)2\frac{1}{2I_1}(I_1\omega_1)^2=\frac{1}{2I_2}(I_2\omega)^2 orL12I1=L22I2\frac{L^2_1}{I_1}=\frac{L^2_2}{I_2} or L1L2=I1I2\frac{L_1}{L_2}=\sqrt{\frac{I_1}{I_2}} but I1=I,I2=2II_1=I,I_2=2I =L1L2=I2I=12,\frac{L_1}{L_2}=\sqrt{\frac{I}{2I}}=\frac{1}{\sqrt{2}}, or L1:L2=1:2L_1:L_2=1:\sqrt{2}