An object of mass 1 kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, g = 10 m s - 2 and radi

Question

An object of mass 1 kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, g = 10 m s - 2 and radius of earth = 6400 km ]

TestHub · Accepted Answer

Gravitational potential energy on the earth surface $U_{i} = \frac{- G M m}{R}$
Gravitational potential energy at a height $h$ above the earth's surface $U_{f} = - \frac{G M m}{R + h} = - \frac{G M m}{R + 3 R} = - \frac{G M m}{4 R}$
Gain in gravitational potential energy
$Δ U = U_{f} - U_{i} = - \frac{G M m}{4 R} + \frac{G M m}{R} = \frac{G M m + 4 G M m}{4 R} = \frac{3 G M m}{4 R}$
Gravitational potential energy in terms of acceleration due to gravity is $∆ U = \frac{3}{4} m g R$
$= \frac{3}{4} \times 1 \times 10 \times 64 \times 10^{5}$
$= 48 MJ$

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