Two spherical bodies of mass M and 5M & radii R & 2R respectively are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smallar body just before collision is

Options

A. 2.5 R
B. 4.5 R
C. 7.5 R
D. 1.5 R

Answer

C

Explanation

Force on M block `F=(GM5m)/(144R^(2))`
`a=(F)/(m)=(5GM)/(144R^(2))`
force on 5 block
`F=(GM5m)/(144R^(2))`
`a=(GM5m)/(144R^(2).5m)=(GM)/(144R^(2))`
Relative acceleration
`a=(5GM)/(144R^(2))+(GM)/(144R^(2))=(6GM)/(144R^(2))=(GM)/(24R^(2))`
`9R=(1)/(2)xx(GM)/(24R^(2))xxt^(2)`
`t^(2)=(18Rxx24R^(2))/(GM)`
`s=(1)/(2)xx(5GM)/(144R^(2))xx(18Rxx24R^(2))/(GM)=7.5R`
OR

system centre of mass situation
`[becausevecF_("system")=0]`
`(M(0)+5M(12E))/(M+5M)=(M(d)+5M(d+3R))/(M+5M)impliesd=7.5R`