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Define gravitational potential energy. Obtain the formula for the gravitational energy of body at distancer r (r gt R_c)fromthe centre of earth. |
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Answer» Solution :`implies` Gravitational potential energy : "The work done in bringing a body of unit mass from infinite distance to the given point in gravitational field of other body is called the gravitational potential energy at that point".  `implies`Suppose, the mass of earth is Mp and radius RE: We have to determine the gravitational potential energy of mass m at point P from distancer from the centre of earth. `implies` Suppose, at any instant body of mass m lying at point A at a distance x from the centre of earth OP = x `implies`The gravitational force on the body at this point, `F = (GM_(E) m)/x^2 ""...(1)` `implies` The work done to MOVE the body to small displacement from the centre of earth dW = FDX `:.dW = (GM_Em)/x^2dx""...(2)` `implies` TOTAL work done to bring the body from infinite (D) distance to x distance `implies W = intdW=int_(oo)^(r)(GM_Em)/x^2dx` `implies W=GM_(E)"m"int_(oo)^(r) x^(-2) dx` `implies W = GM_Em[-1/x]_(oo)^(r)` `implies W=(GM_Em)[-1/r+1/oo]` `:. W=-(GM_Em)/r""...(3)` `implies ` ACCORDING to definition this work done is known as gravitational potential energy of a body of mass m at point P, `U =-(GM_Em)/r""...(4)` If a body bring to at the surface of earth r = Re, `U = - (GM_Em)/(R_E) ""....(5)` |
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