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.

The loss of kinetic energy during the above process is

Answer: (B)

Solution

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.

Initial kinetic energy:

K E_{i} = \frac{1}{2} I (2 ω)^{2} + \frac{1}{2} (2 I) (ω)^{2} = 2 I ω^{2} + I ω^{2} = 3 I ω^{2}

Final kinetic energy (with common angular velocity

ω^{'} = \frac{4 ω}{3}

K E_{f} = \frac{1}{2} (3 I) (\frac{4 ω}{3})^{2} = \frac{1}{2} (3 I) \frac{16 ω ^{2}}{9} = \frac{8 I ω ^{2}}{3}

Loss of kinetic energy:

Δ K E = 3 I ω^{2} - \frac{8 I ω ^{2}}{3} = \frac{9 I ω ^{2} - 8 I ω ^{2}}{3} = \frac{I ω ^{2}}{3}

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