Question

if the mass of a planet is eight times the mass of the earth and its radius is twice the radius of earth, what will be the escape velocity for the planet?

Answer 1

Given in the question :-

Planet mass is 8 times that earth

Planet radius is twice then the radius of earth.

Let mass of the Earth = M

Radius of the Earth = R

Now, we know that The equation to get escape velocity  

v = √(2 g r)

 If the mass of planet is eight times then escape velocity = 2 √2 times. 

Escape velocity reduced to by 1/√2. If radius expands twice

Hence the net escape velocity will be increase.

2 √2 ×  (1/√2)= 2 times now.

Now it is clear that the escape velocity of that planet will be 2 times from the earth.

Escape velocity of the earth = 11.2 km/s

Escape velocity of that planet = 2 × 11.2 = 22.4 km/sec.

Hence the escape velocity of that planet will be 22.4 km/s

Hope it Helps :-)