The amount of work done to raise a mass 'm$m$' from the surface of the Earth to a height equal to the radius of the Earth 'R$R$' will be

Related Formula

Core Logic

The work done by an external force is equal to the change in gravitational potential energy.

Initial Potential Energy (at surface, r = R$r = R$):

Final Potential Energy (at height h = R$h = R$, distance from center r = 2R$r = 2R$):

Step 1: Calculate Work Done

Substitute GM = gR²$GM = gR^2$:

Pattern Recognition

Standard shortcut formula for work done against gravity to height h$h$: W = (mgh)/(1 + h/R)$W = \frac{mgh}{1 + h/R}$. Plugging h = R$h = R$ yields (mgR)/(1 + 1) = (mgR)/(2)$\frac{mgR}{1 + 1} = \frac{mgR}{2}$ instantly.

Chapter Mix

Class 11 Physics: Gravitation Class 11 Physics: Work Energy and Power