Question
What is escape velocity. Derive an expression for the same.
✓
Answer
The minimum velocity required to escape from the gravitational force of earth is called escape velocity. Total energy is the sum of P.E. and K.E.
$\text{T.E}=-\frac{\text{GMm}}{\text{R}}+\frac{1}{2}\text{mv}^2$
To escape K.E should be greater than P.E., i.e..
$\frac{1}{2}\text{mv}^2\geq-\frac{\text{GMm}}{\text{R}}$
$\text{v}_{\text{e}}=\sqrt{2\frac{\text{GM}}{\text{R}}}=\sqrt{2\text{gR}}$
$\text{T.E}=-\frac{\text{GMm}}{\text{R}}+\frac{1}{2}\text{mv}^2$
To escape K.E should be greater than P.E., i.e..
$\frac{1}{2}\text{mv}^2\geq-\frac{\text{GMm}}{\text{R}}$
$\text{v}_{\text{e}}=\sqrt{2\frac{\text{GM}}{\text{R}}}=\sqrt{2\text{gR}}$
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