Gravitation

JEE Main level, numerical answer, medium

138 of 223

Question 138 of 223

The initial velocity vi{v}_{i} required to project a body vertically upward from the surface of the earth to reach a height of 10R10R, where RR is the radius of the earth, may be described in terms of escape velocity ve{v}_{e} such that vi=xy×ve{v}_{i}=\sqrt{\dfrac{x}{y}}\times {v}_{e}. The value of xx will be

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Answer: 10

−GMm11R=−GMmR+12mv2\dfrac{-GMm}{11R}=\dfrac{-GMm}{R}+\dfrac{1}{2}m{v}^{2}
⇒v=20GM11R\Rightarrow v=\sqrt{\dfrac{20GM}{11R}}

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