JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Work, Power & Energy

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 ratio

x_{1} / x_{2}

Answer: (C)

Solution

The potential energy stored in a compressed spring is converted to rotational kinetic energy of the disc.

For disc A:

\frac{1}{2} k x_{1}^{2} = \frac{1}{2} I (2 ω)^{2} = 2 I ω^{2}

For disc B:

\frac{1}{2} k x_{2}^{2} = \frac{1}{2} (2 I) (ω)^{2} = I ω^{2}

Dividing the two equations:

\frac{x _{1}^{2}}{x _{2}^{2}} = \frac{2 I ω ^{2}}{I ω ^{2}} = 2

\frac{x _{1}}{x _{2}} = 2

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