A particle moving with kinetic energy `3J` makes an elastic head-on collision with a stationary particle which has twice its mass. During the impact :-

Options

A. The minimum kinetic energy of system is 1J
B. The minimum elastic potential energy of the system is 2J
C. Momentum and total energy are conserved at energy instant
D. The ratio of kinetic energy to potential energy of the system first decreases and then increases.

Answer

A, B, C, D

Explanation

According to `L.C.E.`
`U_(1)+K_(1)=U_(2)+K_(2)`
`(-GMm)/(r_(1))+K_(1)=(-GMm)/(r_(2))+K_(2)=E`
`(-GMm)/(r_(1))=E-K_(1)to(1)`
`(-GMm)/(r_(2))=E-K_(2)to(2)`
`(r_(2))/(r_(1))=(E-K_(1))/(E-K_(2))`
`:.` If `r_(2)=2r_(1)` then
`(2r_(1))/(r_(1))=(E-K_(1))/(E-K_(2))`
`2E-2K_(2)=E-K_(1)`
`E=2K_(2)-K_(1)`