Question

A body of mass m is takes from earth surface to the height
'h'equal to the redius of earth, the increase is potential energy
will be - mgr / 1/2 mgr/ 2 mgr/1/4mgr​

Answer 1

Answer: 1/2 MgR

Explanation:

In this case we cannot assume the g (gravitational acceleration) to be constant because of very very large distance viz R (radius of the earth)

So, PE gained in this case would be the work done against the gravity to move the object from R to 2R

{R to 2R bcoz it was initially placed on the surface of the earth which is at a distance of R from earth's centre}

Basically we know that W = F•S (Force x displacement)

Here, F = G M1 M2/ R2 which is simply formula for gravitational force, and the displacement = R.

=> W = G M1 M2/ 2R² • R

=> W = G M1 M2 / 2R. which is half of the initial work and equals to the gained PE. = 1/2MgR

You can also directly use the formula:- ∆u = mgh/ {1+h/R}.

Hope this will help you!