Question

Q.3. A constant torque of magnitude 3000Nm changes the angular velocity of a rotating body from 5 rad/s to 20 rad/s in 5 sec. Then the M.I.of the body about the axis of rotation is---- *​

Answer 1

Given:

A constant torque of magnitude 3000Nm changes the angular velocity of a rotating body from 5 rad/s to 20 rad/s in 5 sec.

To find:

Moment of Inertia of body?

Calculation:

General expression of torque is :

$\tau = I \times \alpha$

$\implies \tau = I \times \dfrac{( \omega_{2} - \omega_{1}) }{t}$

$\implies 3000 = I \times \dfrac{(20 -5) }{5}$

$\implies 3000 = I \times \dfrac{15}{5}$

$\implies 3000 = I \times 3$

$\implies I = 1000 \: kg {m}^{2}$

So, value of M.I. is 1000 kgm².