Question

A bucket of water of mass 21 kg is suspended by a rope wrapped around a solid cylinder 0.2 m in diameter. Rope does not slip on the cylinder. The mass of the solid cylinder is 21 kg. The bucket is released from rest. Which of the following statements are correct?

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

Answer 1

Answer: (A), (B), (C), (D)

All of these

210 - T = 21 a
Again, $TR=Ia/R$ (i)

$T=\frac{la}{R^2}=\frac{\frac{1}{2}\times 21\times R^2\times a}{R^2}=\frac{1}{2}\times 21a$
21a = 2T
From Eq. (i), 210 - T = 2T
or 3T = 210
or T = 70 N
Again from Eq. (i), 210 - 70 = 21 a
$a=\frac{140}{21}m{s}^{-2}=\frac{20}{3}m{s}^{-2}$