Question

The escape velocity of a body from the earth is $v_{e}$ . If the radius of earth contracts to $\frac{1}{4}th$ of its value, keeping the mass of the earth constant, the escape velocity will be

• A. doubled
• B. halved
• C. tripled
• D. unaltered

Answer 1

Answer: (A)

doubled

Answer 2

Escape velocity $v_{e}=\sqrt{\frac{2 G M}{R}}$ If $R'=\frac{R}{4}$ $v_{e}'=2 \sqrt{\frac{2 G M}{R}}$ Since, $G$ and $M$ are constant, hence $v_{e}'=2 v_{e}$