Question

Their
21. The angular momentum of two bodies
about some fixed axis are in ratio 1:
moment of inertia about these axis are
1 : 3. Ratio of their kinetic energies is
(1) 1 : 16
(2) 1:9
(3) 3:16
(4) 16:3​

Answer 1

Answer:

Option (3) 3:16

Explanation:

Let the angular momentums of the bodies be $L_1$ and $L_2$ and their moment of inertias are $I_1$ and $I_2$

Given that

$\frac{L_1}{L_2}=\frac{1}{4}$

$\frac{I_1}{I_2}=\frac{1}{3}$

Kinetic Energy is given by

$K=\frac{1}{2}I\omega^2$

But angular momentum $L=I\omega$

Therefore, Kinetic Energy in terms of L and I can be written as

$K=\frac{1}{2}\times I\times (\frac{L}{I})^2$

or, $K=\frac{L^2}{2I}$

Kinetic energy of body (1)

$K_1=\frac{L_1^2}{2I_1}$

Kinetic energy of body (2)

$K_2=\frac{L_2^2}{2I_2}$

Therefore,

Kinetic energy of body (1)

$\frac{K_1}{K_2}=\frac{L_1^2}{2I_1}\times\frac{2I_2}{L_2^2}$

$\implies \frac{K_1}{K_2}=(\frac{L_1}{L_2})^2\times\frac{I_2}{I_1}$

$\implies \frac{K_1}{K_2}=(\frac{1}{4})^2\times\frac{3}{1}$

$\implies \frac{K_1}{K_2}=\frac{3}{16}$

$\implies {K_1}:{K_2}={3}:{16}$

Hope this helps.

Answer 2

Answer:

correct ANSWER is 3:16

Explanation:

This is the easy method for this type of question.....

hope it will help you

Look at this attachment for easy method