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

Answer 1

Answer: (A)

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