Question

Two discs $A$ and $B$ are mounted coaxially on a vertical axle. The discs have moments of inertia $l$ and $2l$, respectively, about the common axis. Disc $A$ is imparted an initial angular velocity $2 \omega$ using the entire potential energy of a spring compressed by a distance $x_{1}$. Disc $B$ is imparted an angular velocity $\omega$ by a spring having the same spring constant and compressed by a distance $x_{2}$. Both the discs rotate in the clockwise direction.
When disc $B$ is brought in contact with disc $A$, they acquire a common angular velocity in time $t$. The average frictional torque on one disc by the other during this period is

• A. $\frac{2 I \omega}{3 t}$
• B. $\frac{9 I \omega}{2 t}$
• C. $\frac{9 I \omega}{4 t}$
• D. $\frac{3 I \omega}{2 t}$

Answer 1

Answer: (A)

The effect moment of inertia is $31$ .
Then from the conservation of angular momentum, we have
$3 l \omega^{\prime}=2 l \omega+12 \omega$
$ \Rightarrow \omega^{\prime}=\frac{4}{3} \omega$
and the torque on the first disc is
$\Gamma=2 l \alpha=\frac{2 I \Delta \omega}{t}=\frac{2 I\left(\omega^{\prime}-\omega\right)}{t}$
Substituting for from first equation, we get
$\Gamma=\frac{2 I \omega}{3 t}$