Skip to content
dronacharya.ai
← IIT-JEE 2007 · Paper 1
PhysicsSingle correct+4 / -1Question 14 of 66

IIT-JEE 2007 · Paper 1, Physics question 14

Passage

Paragraph for Question Nos. 14 to 16

Two discs A and B are mounted coaxially on a vertical axle. The discs have moments of inertia II and 2I2I respectively about the common axis. Disc A is imparted an initial angular velocity 2ω2\omega using the entire potential energy of a spring compressed by a distance x1x_1. Disc B is imparted an angular velocity ω\omega by a spring having the same spring constant and compressed by a distance x2x_2. Both the discs rotate in the clockwise direction.

(The paragraph is not printed in the official archive copy (which reproduces only the questions with their answers); its text is restored from the JEE 2007 question paper.)

The ratio x1/x2x_1/x_2 is

Choose one option
Answer and worked solution

Official answer: C

Energy. Each spring's energy becomes rotational energy:
12kx12=12I(2ω)2=2Iω2,12kx22=12(2I)ω2=Iω2.\tfrac12kx_1^2=\tfrac12I(2\omega)^2=2I\omega^2,\qquad\tfrac12kx_2^2=\tfrac12(2I)\omega^2=I\omega^2.

Ratio. x12x22=2\dfrac{x_1^2}{x_2^2}=2, so x1x2=2\dfrac{x_1}{x_2}=\sqrt2.

(C)