An object is allowed to fall from a height R above the earth, where R is the radius of earth. Its velocity when it strikes the earth’s surface, ignoring air resistance, will be :

Question

An object is allowed to fall from a height R above the earth, where R is the radius of earth. Its velocity when it strikes the earth’s surface, ignoring air resistance, will be :, 2 g R, g R, g R 2, 2 g R

MARKS App · Accepted Answer

As gravitational field is a conservative field and therefore mechanical energy will be conserved. Therefore, Loss in PE = Gain in KE - G M m 2 R - - G M m R = 1 2 m v 2 ⇒ v 2 = G M R = g R as g = G M R 2 ⇒ v = g R

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