Question

A bucket is being lowered down into a wall through a rope passing over a fixed pulley f radius 10 cm. Assume that the rope does not slip on the pulley. Find the angular velocity of the pulley at an instant when the bucket is going down at a speed of 20 cm/s and has a acceleration of $4m{s}^{-2}$.

• A. 4 rad/s
• B. 8 rad/s
• C. 2 rad/s
• D. 20 rad/s

Answer 1

The correct option is C 2 rad/s

Since there is no slipping, the linear speed of rope going down would be equal to the tangential speed of rotation of pulley at all points.

Hence, $v=R\omega$

$⟹\omega =\frac{v}{R}=2rad/s$