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 acceleration 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. $10rad{s}^{-2}$
• B. $20rad{s}^{-2}$
• C. $30rad{s}^{-2}$
• D. $40rad{s}^{-2}$

Answer 1

The correct option is D $40rad{s}^{-2}$

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

Hence, $a=R\alpha$

$⟹\alpha =\frac{a}{R}=40rad/s$