Two spherical bodies of masses M and 5M and radii R and 2R are released in free space with initial separation between their centres equal to 12 R. if they attract each other due to gravitational force only, then the distance convered by the smaller body 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`