Question

A circular disc is rotating about its own axis. An external opposing torque of magnitude $0.04\text{Nm}$ is applied on the disc due to which it comes to rest in $5\text{seconds}$. The magnitude of initial angular momentum of the disc is

• A. $0.8{\text{kg-m}}^2/\text{sec}$
• B. $1{\text{kg-m}}^2/\text{sec}$
• C. $0.2{\text{kg-m}}^2/\text{sec}$
• D. $0.4{\text{kg-m}}^2/\text{sec}$

Answer 1

The correct option is C $0.2{\text{kg-m}}^2/\text{sec}$

Given torque $\tau =0.04\text{N-m}$
$t=5\text{sec}$
Rate of change of angular momentum is equal to the torque applied
$\Rightarrow \tau =\frac{dL}{dt}$
or $\tau =\frac{\Delta L}{\Delta t}=\frac{L_f-L_i}{\Delta t}$
where, $L_f\to$ final angular momentum
$L_i\to$ initial angular momentum

And $L_f=0$ (As disc comes to rest after $t=5\text{sec}$)
$\therefore 0.04=\frac{0-L_i}{5}\Rightarrow L_i=-0.2{\text{kg-m}}^2/\text{sec}$
(negative sign indicates the external torque is opposing the motion)
So, magnitude of initial angular momentum of disc is $0.2{\text{kg-m}}^2/\text{sec}$