Question

As shown below, a uniform disc is mounted to a fixed axle and is free to rotate without friction. A thin uniform rod is rigidly attached to the disc so that it will rotate with the disc. A block is attached to the rod.

Disc : mass = 3m, radius = R, moment of inertia about center $I_D=\frac{3}{2}m{R}^2$

Rod : mass = m, length = 2R, moment of inertia about one end $I_R=\frac{4}{3}m{R}^2$

Block : mass 2m

The system is held in equilibrium with the rod at an angle ${\theta }_0$ to the vertical, as shown above, by a horizontal string of negligible mass one end attached to the disc and the other to a wall.

The tension in the string is

• A. $mgsin{\theta }_0$
• B. $3mgsin{\theta }_0$
• C. $5mgcos{\theta }_0$
• D. $5mgsin{\theta }_0$

Answer 1

The correct option is D

$5mgsin{\theta }_0$

Balancing torque about pivot, (in equilibrium)

$TR=2m\left(2R\right)gsin{\theta }_0+mgRsin{\theta }_0$

$\therefore T=5mgsin{\theta }_0$