Center of MassEasy
Question
Two spherical bodies of mass M and 5 M and radii R and 2 R 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 covered by the smaller body before collision is :
Options
A.4.5 R
B.7.5 R
C.1.5 R
D.2.5 R
Solution
Initial distance between their centers = 12 R
At time of collision the distance between their centers = 3R
So total distance travelled by both =12R-3R = 9R
Since the bodies move under mutual forces, center
of mass will remain stationary so
m1x1 = m2x2
mx = 5m(9R - x)
x = 45R - 5x
6x = 45R
x =
R
Hence option (2)
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