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An object is dropped from height h=2 R o...

An object is dropped from height `h=2 R` on the surface of earth. Find the speed with which it will collide with ground by neglecting effect of air. (Where R is radius of earth, take mass of earth M)

Text Solution

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The intial potential energy `(U_(i))` of object is `U_(i) = -(GMm)/(3R)`
Final potential energy `U_(f) = -(GMm)/R`
By law of conservation of energy , `DeltaKE = - DeltaP.E`
` rArr " " 1/2 mv^(2) = - [U_(f) - U_(i)] = U_(i) -U_(f)`
`rArr 1/2 mv^(2) = -(GMm)/(3R) + (GMm)/R`
`rArr 1/2 v^(2) = (2GM)/(3R)`
` rArr v = sqrt((4GM)/(3R) ) = 2 sqrt((GM)/(3R))`
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