Question

The moment of inertia of a body about a given axis is 1.2 kg-m². Initially, the body is at rest. In order to produce, a rotational kinetic energy of 1500 J, an acceleration of 25 rad/s² must be applied about that axis for a duration of ______.

पर्याय

• 4 s

• 2 s

• 8 s

• 10 s

Answer 1

The moment of inertia of a body about a given axis is 1.2 kg-m². Initially, the body is at rest. In order to produce, a rotational kinetic energy of 1500 J, an acceleration of 25 rad/s² must be applied about that axis for a duration of 2 s.

Explanation:

We know that,

∴ Rotational kinetic energy, E = `1/2lomega^2`

`1500 = 1/2 xx 1.2 xx omega^2`

⇒ `omega = sqrt(3000/1.2)` = 50 rad/s

Also, ω = αt

⇒ t = `omega/alpha = 50/25` = 2 s