The increase in gravitational potential energy of an object of mass m raised from the surface of Earth to a height equal to radius R of Earth is -

Question

The increase in gravitational potential energy of an object of mass m raised from the surface of Earth to a height equal to radius R of Earth is - (A) mgR (B) (m g R/2) (C) (m g R/3) (D) (m g R/4)

Tardigrade Admin · Accepted Answer

Increase in potential energy =(- G M m/2 R)-((- G M m/R))=(G m M/2 R)=(G M/R2)× (m R/2) =g × (1/2)mR=(1/2)mgR

Q. The increase in gravitational potential energy of an object of mass $m$ raised from the surface of Earth to a height equal to radius $R$ of Earth is -

$m g R$

$\frac{m g R}{2}$

$\frac{m g R}{3}$

$\frac{m g R}{4}$

Increase in potential energy
$= \frac{- GM m}{2 R} - (\frac{- GM m}{R}) = \frac{G m M}{2 R} = \frac{GM}{R ^{2}} \times \frac{m R}{2}$
$= g \times \frac{1}{2} m R = \frac{1}{2} m g R$

Q. The increase in gravitational potential energy of an object of mass m raised from the surface of Earth to a height equal to radius R of Earth is -

mgR

2mgR​

3mgR​

4mgR​