Question

A body of M.I. 2 kg m² rotates with an angular velocity of 20 rad/s. When an external torque of 0.5 N m acts on it in the opposite direction, the number of revolutions it makes before it comes to rest is ____________.

Options

• `10/pi`

• `30/pi`

• `50/pi`

• `400/pi`

Answer 1

A body of M.I. 2 kg m² rotates with an angular velocity of 20 rad/s. When an external torque of 0.5 N m acts on it in the opposite direction, the number of revolutions it makes before it comes to rest is `400/pi`.

Explanation:

`alpha = tau/"I" = 0.5/2 = 0.25;`

`"Now,"  omega^2 = omega_0^2 - 2alphatheta;`

`"or"  0 = 20^2 - 2 xx 0.25 theta;`

`theta = 800, 2pi"N" = 800`

`therefore "N" = 800/(2pi) = 400/pi`