IIT-JEE 2007 · Paper 1 · Physics Q15

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PhysicsSingle correct+4 / -1Question 15 of 66

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 $I$ and $2I$ 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.

(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.)

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

\dfrac{2I\omega}{3t}

\dfrac{9I\omega}{2t}

\dfrac{9I\omega}{4t}

\dfrac{3I\omega}{2t}

Answer and worked solution

Official answer: A

Common angular velocity. Both rotate the same way, so angular momentum gives
$\omega_f=\frac{I(2\omega)+2I\omega}{3I}=\frac43\omega.$

Torque on A. Its angular momentum changes by $I\left(2\omega-\frac43\omega\right)=\frac23I\omega$ in time $t$ :
$\tau=\frac{2I\omega}{3t}.$

(A)

Topics:Angular momentum and its conservation Torque and rotational dynamics

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IIT-JEE 2007 · Paper 1, Physics question 15