First slide

Presence on line of symmetry towards heavier mass

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

Difficult

A

7.5 R
B

1.5 R
C

2.5 R
D

4.5 R

Solution

Position of center of mass of the system from m $x_{1} = \frac{5 mx 12 R}{6 m} = 10 R$
when they meet they touch each other and separation between them becomes 3R and center of mass from m
$x_{2} = \frac{5 mx 3 R}{6 m} = 2.5 R$
as center of mass is stationary due to absence of any external force so m moves by a distance of $x_{1} - x_{2} = 7.5 R$

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