JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Gravitation

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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}

)

(A)800 km✓ Correct
(B)1600 km
(C)2133 km
(D)4800 km

Answer: (A)

Solution

Using energy conservation:

- \frac{GM m}{R} + \frac{1}{2} m (\frac{v _{e}}{3})^{2} = - \frac{GM m}{R + h}

. Since

v_{e}^{2} = \frac{2 GM}{R}

, we have

\frac{v _{e}^{2}}{18} = \frac{GM}{9 R}

. Substituting:

\frac{GM}{R + h} = \frac{GM}{R} - \frac{GM}{9 R} = \frac{8 GM}{9 R}

. This gives

R + h = \frac{9 R}{8}

, so

h = \frac{R}{8} = \frac{6400}{8} = 800

km.

JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Single correct option

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