An empty bucket of mass 1 kg attached by a light cord passed over a pulley of a water well is released from rest. If the pulley assembly is assumed to be a uniform solid cylinder of mass 8 kg and free to rotate about its axis without any friction, then the speed of the bucket as it hits the water 16 m below is (take, g = `10ms^(-2)`)

Options

A. `4ms^(-1)`
B. `8ms^(-1)`
C. `16ms^(-1)`
D. `20ms^(-1)`

Answer

B

Explanation

Torque on pulley = `Ialpha`
`rArr" "mgR=(MR^(2)alpha)/2`
`alpha=(2mg)/(MR)`
So, acceleration of rope, `a=Ralpha`
= `R*(2mg)/(MR)=(2mg)/M=(2xx1xx10)/8=10/4ms^(-2)`
Speed of bucket as it falls by 16 m is
`v=sqrt(2xxaxxs)=sqrt(2xx10/4xx16)=sqrt80=8.6~~8ms^(-1)`