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Two spherical bodies of mass M and 5M and radii R and 2R 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 smaller body before collision is
A
2.5R
B
4.5R
C
7.5R
D
1.5R
Detailed Solution
At collision the separation between centres is $R + 2R = 3R$.
Total distance covered by both bodies $= 12R - 3R = 9R$.
Only internal forces act, so the centre of mass stays at rest: $m_1x_1 = m_2x_2$
$Mx = 5M(9R - x) \Rightarrow 6x = 45R$
$x = 7.5R$
Total distance covered by both bodies $= 12R - 3R = 9R$.
Only internal forces act, so the centre of mass stays at rest: $m_1x_1 = m_2x_2$
$Mx = 5M(9R - x) \Rightarrow 6x = 45R$
$x = 7.5R$