Question

3. Two bodies have their moments of inertia I and 21 respectively about their axis of
rotation. If their kinetic energies of rotation are equal, their angular momenta will
be in the ratio
a) 1:2
b) √2:1 c) 2:1
d) 1:√2
​

Answer 1

SOLUTION.

As we for a body in rotation it's kinetic energy can be written as...

K = 1/2 Iw²

Where I is the moment of inertial of the body about it axis of rotation.

w is the angular velocity.

ACC to you Kinetic energy of both the both body is equal.

K(1) = K(2)

1/2.I(1).w² = 1/2.I(2).(w°)²

I(1) = I

I(2) = 2I

w is the angular velocity of first body.

w° is the angular velocity of second body.

I.w² = 2I.(w°)²

w° = w/√2.......EQ(1)

For a body in rotation angular momentum is given as { I×w }

For first body = I×w

For second body = 2×I×w/√2

Ratio = I×w : 2×I×w/√2

Ratio = 1:√2

#answerwithquality

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