A wheel is rotating about an axis through its centre at 720 rpm . It is acted on by a constant torque opposing its motion for 8 seconds to bring it to rest finally . The value of torque ( in N-m ) Is :- (Given `I = (24)/pi kg - m^(2)`)

Options

A. 48
B. 72
C. 96
D. 120

Answer

B

Explanation

In given question torque is constant
So `tau = (L_2-L_1)/(t_2-t_1)... (i)`
L is angular momentum here
Given `t_2- t_1 = 8s, L_1 = Iomega_1 and L_2 = 0`
`omega_1 = 2pin`, here n = 720 rpm
So `n= (720)/60 ` rps = 12 rps
(rps = rotations per second)
So from eq (i)`tau=(0-(24/pi)(2pi(12)))/8`
`tau = -72 Nm `
so `tau = 72` Nm (Opposing Torque)