Question

An object of mass 1 kg is taken to a height from the surface of the earth which is equal to three times the radius of the earth. The gain in potential energy of the object will be ______.

[If, g = 10 ms^-2 and radius of earth = 6400 km]

Options

• 48 MJ

• 24 MJ

• 36 MJ

• 12 MJ

Answer 1

An object of mass 1 kg is taken to a height from the surface of the earth which is equal to three times the radius of the earth. The gain in potential energy of the object will be 48 MJ.

Explanation:

Initial potential energy, U_i = `(-GMm)/R`

Final potential energy, U_f = `-(GMm)/(4R)`

The gain in potential energy of the object will be,

`DeltaU = U_f - U_i = -(GMm)/(4R) + (GMm)/R = (3GMm)/(4R)` (∴ GM = gR²)

= `3/4` mgR = `3/4 xx 1 xx 10 xx 64 xx 10^5 = 48` MJ