A torque of 75 Nm acts on a body at rest for 4 s. What is the change in its angular momentum?

Options

A. increases by `"100 kg m"^(2)//s`
B. decreases by `"200 kg m"^(2)//s`
C. increases by `"200 kg m"^(2)//s`
D. increases by `"300 kg m"^(2)//s`

Answer

D

Explanation

At time t = 0, the body is rest i.e. `omega=0`
Let `omega` be its angular velocity after t = 4s
`therefore alpha=(d omega)/(dt)=(omega)/(t)=(omega)/(4)`
`"M.I. of the body is I and L "=Iomega" "therefore I=(L)/(omega)`
and `tau = Ialpha =(L)/(omega)alpha=(L)/(omega).(omega)/(4)=(L)/(4)`
`thereforeL=4pi=4xx75="300 kg m"^(2)//s`
Thus when the torque is applied, L increases by `"300 kg m"^(2)//s`