Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia $I$ and $2 I$ 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

JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Rotational Mechanics

Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia

I

and

2 I

respectively about the common axis. Disc A is imparted an initial angular velocity

2 ω

using the entire potential energy of a spring compressed by a distance

x_{1}

. Disc B is imparted an angular velocity

ω

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

Answer: (A)

Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia

I

and

2 I

respectively about the common axis. Disc A is imparted an initial angular velocity

2 ω

using the entire potential energy of a spring compressed by a distance

x_{1}

. Disc B is imparted an angular velocity

ω

by a spring having the same spring constant and compressed by a distance

x_{2}

. Both the discs rotate in the clockwise direction.

When the discs come in contact, angular momentum is conserved:

I (2 ω) + 2 I (ω) = (I + 2 I) ω^{'} = 3 I ω^{'}

ω^{'} = \frac{4 ω}{3}

For disc B, the change in angular velocity is from

ω

\frac{4 ω}{3}

ω^{'} = ω + \frac{τ}{2 I} t

\frac{4 ω}{3} = ω + \frac{τ}{2 I} t

\frac{ω}{3} = \frac{τ t}{2 I}

τ = \frac{2 I ω}{3 t}

JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Single correct option