2 SPHERICAL BODIES OF MASS M AND 5M WITH RADII R AND2R

ARE RELEASED IN FREE SPACE WITH INITIAL SEPARATION =12R. IF THEY ATTRACT EACH OTHER DUE TO GRAVITATIONAL FORCE ONLY THEN THE DISTANCE COVERED BY THE SMALLER BODY JUST BEFORE COLLISION IS?????

ANS.7.5R

dear akhilesh , first u draw the figure according to steps ,

1) draw x axis & y axis ...

2)place small sphere such that its center lies at origin & big sphere such its center lies at 12R distance on +x axis....

3)let these sphere collide at a point (X,0) .... (X is the center of small sphere)

now distance of center of small sphere from origin is X &

  distance of big sphere from origin is (X+3R) ....

now we know that the spheres are moving due to their internal forces only or we can say no external force is acting on the system so center of mass of system remains at same position...

initially center of mass = [M(0) + 5M(12R)]/6M               ..................1

finally center of mass = [M(X) + 5M(X+3R)]/6M              ...............2

equating 1 & 2 we get

 5M(12R) = MX + 5M(X+3R)         OR

X = 7.5R

Approved