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 statement(s) is/are correct?

Options

A. The tension in the rope is 70 N.
B. The acceleration of the bucket is (20/3) m/`s^(2)`
C. The acceleration of the bucket is independent of the mass of the bucket.
D. The tension in the rope is 50 N.

Answer

A, B, C

Explanation

From the free body diagram we can write that, mg- T= ma
210- T= 21a ….(i)
Again `tau- =Ialpha`
`rArrTR=(la)/R`
`rArrT=(Ia)/(R^(2))=(1/2xx21xxR^(2)xxa)/(R^(2))`
`=1/2xx21a`
`21a=2T`
From eq.(i) 210-T=2T
or 3T= 210 or T= 70 N
Again from eq.(i), 210 - 70 = 21a
`a=(140)/21ms^(-2)=20/3ms^(-2)`