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Derive an explain escape velocity . v = √2gr​ plzz answer correctly.... don't spam... answer in long....

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VelocityIt is the minimum velocity required for a particle to escape from the gravitational field of the earth, and it is expressed as,PROOF for the Expression of the Escape Velocity:-Consider a particle of mass which has to be projected from the surface of earth of mass and radius The force required to escape the particle from the gravitational field of the earth is equal to the gravitational force of ATTRACTION of the particle due to the earth, i.e.,The work done to project the particle outside the earth by a small distance is,Then the TOTAL work done to project the particle from the surface of the earth to infinity is,This work done is stored in the particle as its kinetic energy. Therefore,But,Then (1) becomes,



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