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

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

1. A

the total mechanical energy of the two objects is zero.

2. B

their relative velocity is $\sqrt{\frac{10\mathrm{Gm}}{\mathrm{r}}}$.

3. C

the total kinetic energy of the system of objects is $\frac{4{\mathrm{Gm}}^{2}}{\mathrm{r}}$.

4. D

their relative velocity is zero.

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### Solution:

For (A) : By COME total mechanical energy of the two objects remains same. Initially , both potential and kinetic energy is zero.
For (B) : By using reduced mass concept

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