A certain planet has an escape speed V.If another planet has twice size and twice the mass of the first planet,its escape speed will be
A) 2V.
B) V.
C) V.
D) V/2.
E) V/ .

Question

A certain planet has an escape speed V.If another planet has twice size and twice the mass of the first planet,its escape speed will be
A) 2V. 
B) V. 
C) V. 
D) V/2. 
E) V/ .

Quizplus · Accepted Answer

The escape velocity from a planet is given by the formula:
V = √(2GM/R)
where G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet.

If the second planet has twice the size and twice the mass of the first planet, then its radius will be twice that of the first planet, i.e. R2 = 2R1. Similarly, its mass will be twice that of the first planet, i.e. M2 = 2M1.

Substituting these values in the formula for escape velocity, we get:
V2 = √(2G(2M1)/(2R1))
V2 = √(2G(M1)/R1)
V2 = V

Therefore, the escape speed of the second planet will be the same as that of the first planet, which is V. Thus, the answer is option (C).

A Certain Planet Has an Escape Speed V