Two masses m and 2m are attached to two ends of an ideal spring as shown in figure. When the spring is in the compressed state, the energy of the spring is 60 J, if the spring is released, then at its natural length

Options

A. energy of smaller body will be 20 J
B. energy of smaller body will be 40 J
C. energy of smaller body will be 10 J
D. energy of both the bodies will be same

Answer

B

Explanation

(b) According to law of conservation of momentum,
`mv_(1)+2mv_(2)=0" or "v_(2)=-(v_(1))/(2) " " ...(i)`
According to law of converation of energy,
`(1)/(2)mv_(1)^(2)+(1)/(2)2mv_(2)^(2)=60`
`rArr " " (1)/(2)mv_(1)^(2)+m((-v_(1))/(2))^(2)=60rArr(1)/(2)mv_(1)^(2)+(1)/(2)=60`
`rArr " "(3mv_(1)^(2))/(4)=60 rArr(1)/(2)mv_(1)^(2)=40J`