The moment of inertia of a body about a given axis is `12 kg.m^(2)`. Initially, the body is at rest. In order to produce a rotational kinetic energy of 15000J, an angular acceleration of `10 rads^(-2)` must be applied about that axis for a duration of

Options

A. 2s
B. 4s
C. 10s
D. 5s

Answer

D

Explanation

Given, moment of inertia, `I = 12kg -m^(2)`
Rotational kinetic energy, `E_(k) = (1)/(2) I omega^(2)`
`15000 J = (1)/(2) xx 12 xx omega^(2)`
So, `omega = sqrt((30000)/(12)) = sqrt2500 = 50` rad/s
Angular acceleration, `alpha = 10 rad//s^(2)`
As `alpha = (omega)/(t)`
So, time `= (omega)/(alpha) = (50)/(10) = 5s`