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Gravitation

A body of mass m is moved to a height h equal to the radius of earth. The increase in potential energy is..

Quote:

Originally Posted by subhan2010

a body of mass m is moved to a height h equal to the radius of earth. the increase in potential energy is....?

The increase in PE is equal to the work performed on the body , which is:

$W = \int_a^b \vec F \cdot \vec ds$ .

The force $\vec F$ is the force due to gravity, which is

$<br /> \vec F = \frac {GMm}{r^2}<br />$

So the integral becomes
$<br /> \Delta PE = \int _a ^ b \frac {GMm} {r^2} dr =\frac { GMm} a - \frac {GMm} b<br />$

Here a = radius of earth and b = 2 times radius of earth.

Its an mcq... here ans written is 1/2 mgR

Quote:

Originally Posted by subhan2010

its an mcq....here ans written is 1/2 mgR

I don't know what an "mcq" is, but 1/2 mgR is equivalent to what I wrote. Sub R for a, 2R for b, and recall that g = GM/R^2.

Multiple choice question... thank u... my mistake.