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Q.

A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be:
(Take radius of earth = 6400 km and g = 10 ms^–2 )

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a

4800 km

b

1600 km

c

800 km

d

2133 km

answer is A.

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Detailed Solution

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$\begin{array}{l} v_{e} = \sqrt{\frac{2 Gm}{R}} \\ \frac{- GMm}{R} + \frac{1}{2} m \frac{V_{e}^{2}}{9} = - \frac{GMm}{R + h} \\ \frac{GM}{R + h} = \frac{GM}{R} - \frac{V_{e}^{2}}{18} \\ \frac{GM}{R + h} = \frac{GM}{R} - \frac{GM}{9 R} \\ \frac{GM}{R + h} = \frac{8 GM}{9 R} \\ \frac{1}{R + h} = \frac{8}{9 R} \\ 9 R = 8 R + 8 h \\ h = \frac{R}{8} \Rightarrow \frac{6400}{8} \Rightarrow 800 km \end{array}$

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