Two particles each of mass m are revolving in circular orbits of radius 5R in opposite directions around earth of radius R. They collide perfectly inelastically and fall to ground. The speed of combined mass on striking the ground will be.

# Two particles each of mass m are revolving in circular orbits of radius 5R in opposite directions around earth of radius R. They collide perfectly inelastically and fall to ground. The speed of combined mass on striking the ground will be.

1. A

$\sqrt{\frac{GM}{R}}$

2. B

$\sqrt{\frac{3GM}{2R}}$

3. C

$\sqrt{\frac{8GM}{5R}}$

4. D

$\sqrt{\frac{2GM}{R}}$

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### Solution:

$\frac{1}{2}\left(2m\right){V}^{2}=\frac{GM\cdot \left(2m\right)}{R}-\frac{GM\cdot \left(2m\right)}{5R}$'

$v⇒\sqrt{\frac{8GM}{5R}}=2\sqrt{2}\sqrt{\frac{GM}{5R}}$

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