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Q.

A particle is projected vertically upwards with a speed V₀ from the surface of the earth. The maximum height reached by the particle is equal to radius R of the earth. If g be the acceleration due to gravity on the surface of the earth, then :

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a

$v_{0}^{2} = 2 gR$

b

$v_{0}^{2} > 2 gR$

c

$v_{0}^{2} = gR$

d

$v_{0}^{2} < 2 gR$

answer is D.

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Detailed Solution

$- mgR + \frac{1}{2} {mv}_{0}^{2} = - \frac{mgR}{2} + 0 \Rightarrow v_{0}^{2} = gR$

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