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Q.

The escape speed for a projectile in the case of earth is 11.2 km/sec. A body is projected from the surface of the earth with a velocity which is equal to twice the escape speed. The velocity of the body when at infinite distance from the centre of the earth is-

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a

11.2 km/sec

b

22.4 km/sec

c

11.2 $\sqrt{3}$ km/sec

d

11.2 $\sqrt{2}$ km/sec

answer is C.

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Detailed Solution

Form energy conservation $\frac{1}{2} m v^{2} = \frac{1}{2} {mv}_{e}^{2} + \frac{1}{2} {mv}^{' 2} \Rightarrow v^{2} = v_{e}^{2} + v^{' 2}$
$V^{' 2} = (2 \times 11 .2 - 11 .2) (2 \times 11 .2 + 11 .2) \Rightarrow V^{2} = 11 .2 \times 11 .2 \times 3 \Rightarrow V^{'} = 11 .2 \sqrt{3}$

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