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An object is allowed to fall freely towards the earth from a distance r ( gt R_e)from the centre of the earth. Find the speed of the object when it strikes the surface of the earth. |
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Answer» Solution : Initial speed of BODY is zero, HENCE total energy, `E=(GM_em)/R "" .......(1)` Suppose mass of body is ` m_1`mass of earth `M_(e)`radius of earth `R_eand v`is the speed of body when it hit the earth. Total energy of body when body hit the earth, `E = 1/2 mv^(2) - (GM_(e)m)/R_e ""..........(2)` Neglecting air resistance, according to conservation of MECHANICAL energy, `1/2mv^2-(GM_em)/R_e=(GM_em)/r` `:.v^2=2GM_e(1/R_e-1/r)` but `g = (GM_e)/R_e^2` `:. v^2=2R_e^2g(1/R_e-1/r)` or `:. v =R_e[2g(1/R_e-1/r)]^(1/2)` |
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