## Question

A particle falls on the surface of the earth from infinity. If the initial velocity of the particle is zero and friction due to air is negligible, find the velocity of the particle when it reaches the surface of the earth. Also find its kinetic energy. (Radius of earth is 6400 km and *g* is 9.8 m/s^{2}.)

### Solution

A particle projected up with the escape velocity *v _{e}* will go to infinity. Therefore, the velocity of the particle falling on the earth from infinity will be

*v*. Now, the escape velocity on the earth is

_{e}

The kinetic energy acquired by the particle is

#### SIMILAR QUESTIONS

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*G*= 6.67 × 10

^{ –11}Nm

^{2}kg

^{–2}.

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