Question

Find the height to which it rise above the earth surface if a particle is projected vertically upwards from the surface of the earth of radius R with kinetic energy equal to half of the minimum value needed for it to escape

Answer 1

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>>A particle is projected vertically upwar

Question



A particle is projected vertically upward from the surface of earth (radiusRe) with a kinetic energy equal to half of the minimum value needed for it to escape.The height to which it rises above the surface of earth is

A

h=Re

B

h=2Re

C

h=Re/2

D

h=3Re

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Solution



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Correct option is A)

The kinetic energy needed to escape from the surface is given as,

E=21mve2

=21m(Re2Gm)2

=ReGMm

Since, the potential energy at the maximum height will be equal to the sum of half kinetic energy and the potential energy at the surface of the earth.

It can be written as,

−ReGMm+21ReGMm