A stationary object is divided into two fragment of mass 2M and 3M. Total energy of both fragment is E. Find energy of fragment with mass 2M.

Options

A. `(2E)/(5)`
B. `(E )/(2)`
C. `(E )/(5)`
D. `(3E)/(5)`

Answer

D

Explanation

By law of conservation of energy
`(M_(1) +M_(2) ) V=2Mv_(1) - 3M v_(2)`
Where `M_(1) =2M ,M_(2) = 3M V=0`
`2Mv_(1) =3M_(2)`
`v_(2) =(2)/(3) v_(1)`
`v_(2)^(2) = (4)/(9) v_(1)^(2)`
Total energy
`E= (1)/(2) .(2M)v_(1)^(2) + (1)/(2) (3M)v_(2)^(2)`
`=mv_(1)^(2) + (3)/(2) Mv_(2)^(2)`
`=mv_(1)^(2) + (2)/(3) Mv_(1)^(2)`
`E= (5)/(3) Mv_(1)^(2)`
Kinetic energy of 2M part
`E_(1) = (1)/(2) (2M) v_(1)^ (2)`
Taking ratio of (2) and (3) `(E_(1))/(E ) = ((1)/(2) (2M)v_(1)^(2))/((5)/(3)Mv_(1)^(2))`
`E_(1) = (3)/(5)E`