particles of masses 2M m and M are resectively at points A , B and C with ` AB = (1)/(2) (BC)` m is much - much smaller than M and at time ` t=0` they are all at rest as given in figure . As subsequent times before any collision takes palce .

Options

A. m will remain at rest
B. m will move towards M
C. m will move towards 2M
D. m will have oscillatory motion

Answer

C

Explanation

Force on B due to `A=F_(BA)=(G(2Mm))/((AB)^2)` towards BA
Force on B due to `C=F_(BC)=(GMm)/((BC)^2)` towards BC
As, (BC)=2AB
`rArrF_(BC)=(GMm)/((2AB)^2)=(GMm)/(4(AB)^2)ltF_(BA)`
Hence, m will move towards BA (i.e., 2M )