1. Tardigrade
  2. Question
  3. Physics
  4. The initial velocity vi required to project a body vertically upward from the surface of the earth to reach a height of 10 R, where R is the radius of the earth, may be described in terms of escape velocity v e such that vi=√(x/y) × v e . The value of x will be

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Q. The initial velocity $v_{i}$ required to project a body vertically upward from the surface of the earth to reach a height of $10 R$, where $R$ is the radius of the earth, may be described in terms of escape velocity $v_{ e }$ such that $v_{i}=\sqrt{\frac{x}{y}} \times v_{ e } .$ The value of $x$ will be ______

JEE MainJEE Main 2021Gravitation

Solution:

$\frac{- GMm }{11 R }=\frac{- GMm }{ R }+\frac{1}{2} mv ^{2}$
$v =\sqrt{\frac{20 GM }{11 R }}$