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

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The tension in the rope is 70 N.

The acceleration of the bucket is $(20 / 3) m / s^{2}$

The acceleration of the bucket is independent of the mass of the bucket.

The acceleration of the bucket is (10/3)m/s²

answer is A, B, C.

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Detailed Solution

$210 - T = 21 a$ …(i)

Again, $τ = Iα$

$TR = \frac{Ia}{R}$

$T = \frac{Ia}{R^{2}} = \frac{\frac{1}{2} \times 21 \times R^{2} \times a}{R^{2}}$

$= \frac{1}{2} \times 21 a$

$21 a = 2 T$

From Eq. (i), $210 - T = 2 T$

or $3 T = 210$

or $T = 70 N$

Again from Eq. (i), $210 - 70 = 21 a$

$a = \frac{140}{21} {ms}^{- 2} = \frac{20}{3} {ms}^{- 2}$

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