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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 : <img alt="\mathrm

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 :

\mathrm{\text { (Take radius of earth }=6400 \mathrm{~km} \text { and } \mathrm{g}=10 \mathrm{~ms}^{-2} \text { ) }}

Option: 1

\mathrm{800 \mathrm{~km}}


Option: 2

\mathrm{1600 \mathrm{~km}}


Option: 3

\mathrm{2133 \mathrm{~km}}


Option: 4

\mathrm{4800 \mathrm{~km}}


Answers (1)

best_answer

\mathrm{ u=\frac{V_e}{3} }
We know that, \mathrm{V_e=\sqrt{\frac{2 G M}{R}}}
By energy conservation, TE at surface = TE at maximum

\mathrm{\left.\frac{1}{2} m u^2+\left[(\frac{-G M m}{R}\right)\right]=\frac{1 m}{2}(0)^2+\left(\frac{-G M m}{R+h} )\right. }

\mathrm{\frac{8 G M m}{9 R}=\frac{G M m}{R+h}}

\mathrm{h=\frac{R}{8}=800 \mathrm{~km}}

Hence (1) is correct option.

Posted by

Nehul

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