First slide

Gravitaional potential energy

Question

The gravitational potential energy of a rocket of mass 100 kg at a distance 10⁷ m from the earth's mass is 4.8 x 10⁹ joule. The weight of the rocket in newton at a distance 10⁹m is

Moderate

A

$8 \times 10^{- 2}$
B

$8 \times 10^{- 3}$
C

$4 \times 10^{- 3}$
D

$4 \times 10^{- 2}$

Solution

$U = \frac{GMm}{Rr} or GM = \frac{Ur}{m}$ ……………….(1)
weight at a distance r
$= mg = m \frac{GM}{R^{2}}$ ……………………(2)
$\begin{aligned} ∴ W = m \frac{1}{R^{2}} \cdot \frac{Ur}{m} = \frac{Ur}{R^{2}} \\ = \frac{(4 \times 10^{9}) (10)^{7}}{{(10^{9})}^{2}} = 4 \times 10^{- 2} \end{aligned}$

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