Gravitational potential energy Assignment Help

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Gravitational Potential Energy: The gravitational potential energy of a body at a point is defined as the amount of work done in bringing the body from infinity to that point against the gravitational force.


1246_Gravitational potential energy.png

903_Gravitational potential energy1.png

W=-GMm/r

This work done is stored under the object as its gravitational potential energy                 

            U = - GMm/r

(i) Potential power is a scalar quantity.

(ii) Unit: Joule

(iii) Dimension: [ML2T-2]

(iv) Gravitational potential power is usually negative in the gravitational field because the force is always attractive in nature.

(v) As the distance r raise, the gravitational potential energy converts less value i.e., it increases.

(vi) If r =∞ then it becomes zero (maximum)

(vii) In case of discrete distribution of masses

            Gravitational potential energy  300_Gravitational potential energy2.png

(viii) If the body of mass m is rotate from a point at a distance r1 to a point at distance r2(r1 > r2) then change in potential energy

374_Gravitational potential energy3.png

            As r1 is greater then r2, the change in potential energy of the body will be negative. It seems that if a body is brought closer to earth it's potential energy decreases.

(ix) Relation in between potential gravitational energy and potential 

                2082_Gravitational potential energy4.png

         U = mV

(x) Gravitational potential power at the origin of earth relative to infinity.

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(xi) Gravitational potential energy of an object at height h from the earth surface is given by

         230_Gravitational potential energy6.png

 

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