gravitation

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

 ebaines Posts: 10,131, Reputation: 5584 Expert #2 Jun 15, 2012, 06:15 AM
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

$
\vec F = \frac {GMm}{r^2}
$

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

Here a = radius of earth and b = 2 times radius of earth.
 subhan2010 Posts: 39, Reputation: 1 Junior Member #3 Jun 15, 2012, 06:21 AM
its an mcq....here ans written is 1/2 mgR
 ebaines Posts: 10,131, Reputation: 5584 Expert #4 Jun 15, 2012, 06:42 AM
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.
 subhan2010 Posts: 39, Reputation: 1 Junior Member #5 Jun 15, 2012, 09:51 AM
multiple choice question.... thank u...my mistake.

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