## Question

With what velocity must a body be thrown upward from the surface of the earth so that it reaches a height of 10 *R _{e}*? Earth’s mass and

*G*= 6.67 × 10

^{ –11}Nm

^{2}kg

^{–2}.

### Solution

Let *m* be the mass of the body. The gravitational potential energy of the body at the surface of the earth is

The potential energy at a height *h* = 10 R_{e} above the surface of the earth will be

∴ increase in potential energy is

This increase will be obtained from the initial kinetic energy given to the body. Hence if the body be thrown with a velocity *v*, then

Substituting the given values, we get

#### SIMILAR QUESTIONS

Calculate the velocity of projection of a particle so that the maximum height attained by the particle is 0.5 *R _{e}*, where

*R*is radius of earth. The mass of earth is

_{e}*M*.

_{e}
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(Mass of earth = 6.0 × 10^{24} kg, *G* = 6.67 × 10^{–11} Nm^{2} kg^{ –2}).

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