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Q.

The initial velocity vi required to project a body vertically upward from the surface of the earth to reach a height of 10R, where R is the radius of the earth, may be described in terms of escape velocity ve such that  vi=xy×ve. The value of x will be——

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answer is 10.

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Detailed Solution

Conservation of energy, Ui+Ki=Uf+Kf⇒−GMmR+12mvi2=−GMm11R+0 If vi=kv⇒12k2ve2=1011GMR Put ,ve=2GMR⇒12k22GMR=1011GMR⇒k2=1011 As per question, k=xy⇒k2=1011=xy So, x=10
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