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Work Done Against Gravity - Practice Questions & MCQ

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

Quick Facts

  • Work Done Against Gravity is considered one the most difficult concept.

  • 11 Questions around this concept.

Solve by difficulty

If  g  is the acceleration due to gravity on the earth's surface,  the gain in the potential energy of an object of mass  m   raised from the surface of the earth to  a height equal to the radius  R   of the earth is :

Concepts Covered - 1

Work Done Against Gravity

The gravitational potential energy at height 'h' from the earth's surface

Is given by U_{h}=-\frac{mgR}{1+\frac{h}{R}}

So at the surface of earth put h=0

We get U_s=-mgR

So if the body of mass m is moved from the surface of earth to a point at height h from the earth's surface

Then there is a change in its potential energy.

And this change in its potential energy is known as work done against gravity to move the body from earth surface to height h.

W=\Delta U=GMm\left [ \frac{1}{r_{1}}-\frac{1}{r_{2}} \right ]

Where W \rightarrow work done

\Delta U \rightarrow change in Potential energy

r_{1},r_{2}\rightarrow distances

 

Putting r1=R , and r2=R+h

So W=\Delta U=GMm\left [ \frac{1}{R}-\frac{1}{R+h} \right ]

  1. when 'h' is not negligible

              W=\frac{mgh}{1+\frac{h}{R}}

 

 

  1. when 'h' is very small

         As W=\frac{mgh}{1+\frac{h}{R}}

           But h is small as compared to earth's radius

 

         \frac{h}{R}\rightarrow 0

           So W=mgh

 

  1. If h = nR then 

           W=mgR*\frac{n}{n+1}

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Work Done Against Gravity

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