Question

Through what angle will it have rotated when the man reaches his initial position on the turntable?

• A. the table rotates through $2\pi /11$ radians anticlockwise
• B. The table rotates through $4\pi /11$ radians clockwise
• C. The table rotates through $4\pi /11$ radians anticlockwise
• D. The table rotates through $2\pi /11$ radians clockwise

Answer 1

The correct option is D The table rotates through $2\pi /11$ radians clockwise

$w=0.05$ $rad/s$ (solved earlier)

When man reaches its initial position, table rotates with an angle $\theta$ clockwise.

Angular velocity of man, $w_m=\frac{v_o}{r}=\frac{1}{2}=0.5$ $rad/s$

Now, $\theta =wt=0.05t$ and $2\pi -\theta =w_{m}t$

$2\pi -\theta =0.5t$

Solving, $2\pi -\theta =0.5\times \frac{\theta }{0.05}$

$⟹\theta =\frac{2\pi }{11}$ radians clockwise