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Two objects of masses m and 4m are at rest at an infinite separation. They move towards each other under the mutual gravitational attraction. If G is the universal gravitational constant, then at a separation r

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The T.E of two objects is zero

The relative velocity is

{(\frac{10Gm}{r})}^{\frac{1}{2}}

in magnitude

Total K.E’s of the objects is

\frac{{4Gm}^{2}}{r}

Their relative velocity is zero

answer is C.

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Detailed Solution

When two objects of

$m_{1} = m, m_{2} = 4 m$ are at infinite separation $d = \propto$

$G .P .E U_{i} = 0$

When they move due to mutual attraction up to $d = r$

$G .P .E U_{f} = \frac{- 4 {Gm}^{2}}{r}$

Change in PE = Total K.E $= \frac{4 {Gm}^{2}}{r}$

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