The magnitude of gravitational potential energy of a body at a distance ' R ' from the centre of the earth is ' E '. Its weight at a distance ' 1.5 R ' from the centre of

Question

The magnitude of gravitational potential energy of a body at a distance ' R ' from the centre of the earth is ' E '. Its weight at a distance ' 1.5 R ' from the centre of the earth is

TestHub · Accepted Answer

The magnitude of gravitational potential energy of a body of mass $m$ at a distance $R$ from the centre of the earth is given by:

$E = \frac{GM m}{R}$

$\Rightarrow GM m = ER$

The weight of the body at a distance $r$ from the centre of the earth is the gravitational force acting on it:

$W = \frac{GM m}{r ^{2}}$

At a distance $r = 1.5 R = \frac{3}{2} R$ , the weight becomes:

$W = \frac{GM m}{( \frac{3}{2} R ) ^{2}} = \frac{4 GM m}{9 R ^{2}}$

Substituting $GM m = ER$ into the above equation, we get:

$W = \frac{4 ( ER )}{9 R ^{2}} = \frac{4 E}{9 R}$

Answer: $\frac{4 E}{9 R}$

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