Question

A bucket of water of mass $21kg$ is suspended by a rope wrapped around a solid cylinder $0.2$ m in diameter. The mass of the solid cylinder is $21kg$. The bucket is released from rest. Which of the following statements are correct ?

• A. The tension in the rope is $70N$
• B. The acceleration of the bucket is $\left(\frac{20}{3}\right)m/s^2$
• C. The acceleration of the bucket is $\left(\frac{40}{3}\right)m/s^2$
• D. The Tension in the rope is $140N$

Answer 1

Answer: (A), (B)

The correct options are
A The tension in the rope is $70N$
B The acceleration of the bucket is $\left(\frac{20}{3}\right)m/s^2$

Writing Force equation ,
$210-T=21a$
Balancing the torque , $TR=I\alpha$
$TR=\frac{I\alpha }{R}$
$T=\frac{I\alpha }{R^2}=\frac{\frac{1}{2}21R^2\alpha }{R^2}$
$⟹2T=21a$
Replacing this in the force equation ,
$210-T=2T$
$3T=210⟹T=70N$
$2T=21\times \alpha ⟹\alpha =\frac{140}{21}=\frac{20}{3}m{s}^{-2}$