Planets has a mass and radius . Planet has half the mass and half the radius of planet . If the escape velocities from the planets and are and respectively, then surfaces is , the value of is :
Step 1: Given Data:
Mass of planet A
The radius of planet A
Mass of planet B
The radius of planet B
Escape velocities of planet A and planet B is and respectively
It is given that,
Step 2: Formula Used:
The escape velocity is defined as-
Escape velocity
Where is the gravitational constant
are mass of the planet and radius of the planet respectively
Step 3: Calculation of velocity:
According to the formula the escape velocity of planet A is expressed as-
…….(1)
The escape velocity of planet B is expressed as-
On dividing equation (1) by equation (2) we get-
It is given that,
So,
Thus, the value of is .
Hence option C is the correct answer.