Question 275: Gravitation

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

Accepted Answer

Step 1: Recall expressions
Gravitational potential energy of a body of mass $m$ at distance $r$ from Earth's centre:
$ U = -\frac{GMm}{r}. $
So, the magnitude is:
$ |U| = \frac{GMm}{r}. $
Weight (force of gravitation) at distance $r$:
$ F = \frac{GMm}{r^2}. $
Step 2: Relating to the given $E$
At $r = R$, the magnitude of potential energy:
$ E = \frac{GMm}{R}. $
So:
$ GMm = E R. $
Step 3: Force at $r = 1.5R$
At $1.5R$:
$ F = \frac{GMm}{(1.5R)^2} = \frac{ER}{(1.5R)^2} = \frac{E}{(1.5^2 R)}. $
Since $1.5^2 = 2.25 = 	frac{9}{4}$,
$ F = \frac{E}{	frac{9}{4}R} = \frac{4E}{9R}. $
Step 4: Match with options
That corresponds to
Option C
:
$ \boxed{	frac{4E}{9R}} $

Answer

$\frac{2 \mathrm{E}}{9 \mathrm{R}}$

Answer

$\frac{4 E}{5 R}$

Answer

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

Answer

$\frac{2 E}{7 R}$

Gravitation

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

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