Two particles of mass m and M are initially at rest and infinitely separated from each other. Due to mutual interaction, they approach each other.
Their relative velocity of approach at a separation d between them, is

Options

A. `[(2" Gd")/("M "+" m")]^(1//2)`
B. `[(2" G"(M+m))/(d)]^(1//2)`
C. `(2" GM"+m)/(d)`
D. None of these

Answer

B

Explanation

Using the concept of reduced mass
`(-GMm)/(d)+(1)/(2)mu v_(r)^(2)=0" "…(i)`
Here, `" "mu=(mM)/((m+M))`
Hence, `v_(r)=sqrt((2G(m+M))/(d))`