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A bag of sand of mass M is suspended by ...

A bag of sand of mass M is suspended by a roap. A bullet of mass m. traveling with speed v gets. embedded in it. The loss of kinetic energy is

A

`Mmv //(M + m)`

B

`(M + m)//Mmv`

C

`(Mmv^2)/(2(M + m))`

D

`(2(M + m))/(Mv^2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Linear momentum is conserved.
`(M + m) v.= mv`
`:. v. = (mv)/(M+m)`
`KE =1/2 (M + m)v^2`
`:. KE =1/2 (M+m) (m^2v^2)/((M+m)^2) =1/2(m^2v^2)/((M+m))`
Loss of KE = KE of bullet - KE of embedded bag
`=1/2mv^2-1/2(m^2v^2)/(M+m)=(mMv^2)/(2(M+m))`
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