Two objects of masses `m` and `4m` are at rest at an infinite separation. They move towards each other under mutual gravitational attraction. If `G` is the universal gravitaitonal constant, then at separation `r`

Options

A. the total mechanical energy of the two objects is zero
B. Their relative velocity is `sqrt((10GM)/r`
C. the total kinetic energy of the objects is `(4Gm^(2))/r`
D. their relative velocity is zero.

Answer

A, B, C

Explanation

At infinity total mechanical energy was zero, since mechanical energy remain conserve, thus total mechanical energy will be zero through the motion of the particles. K.E.+P.E.=0 Rightarrow K.E.=-P.E.
`Rightarrow1/2(mumv_(rel)^(2))/(m+um)=(Gum^(2))/r`
`Rightarrowv_(rel)=sqrt((10Gm)/r)`