Question

A certain planet has an escape speed V. If another planet has twice the radius and twice the mass of the first planet, its escape speed will be
1. V.
2. V/ 2
3. √.2
4. √ V.
5. 2V.

Answer 1

Answer:

option A

Explanation:

Escape velocity of the planet

       $v = \sqrt{\dfrac{GM}{R}}$

now, it is given that

Second Planet

R₂ = 2R          and M₂ = 2M

now escape velocity of the second planet

now,

       $v'= \sqrt{\dfrac{G(2M)}{(2R)}}$

on solving

       $v'= \sqrt{\dfrac{GM}{R}}$

       $v'= v$

escape velocity of the second planet is equal to first.

The correct answer is option A