In the system shown in figure, mass m is released from rest from position A. Suppose potential energy of m at point A with respect to point B is E. Dimensions of m negligible and all surfaces are smooth. When mass reaches at point B.

Answer

A, B, C, D

Explanation

`mgR=E=(1)/(2)mv_(1)^(2)+(1)/(2)mv_(2)^(2)`
`2mv_(2)=mv_(1)rArrv_(1)=2v_(2)`
`E=(1)/(2)mxx4v_(2)^(2)+mv_(2)^(2)=3mv_(2)^(2)`
`v_(2)=sqrt((E)/(3m)),v_(1)=2sqrt((E)/(3m))`
`"KE of m"=(1)/(2)mv_(1)^(2)+(1)/(2)mxx(4E)/(3m)=(2E)/(3)`
`"KE os 2m"=(1)/(2)2mxxv_(2)^(2)=mxx(E)/(3m)=(E)/(3)`
`P_(1)=mv_(1)=2msqrt((E)/(3m))=sqrt((4)/(3)mE)`
`P_(2)=2mv_(2)=2msqrt((E)/(3m))=sqrt((4)/(3)mE)`