Question

The radius of planet A is half the radius of planet B. If the mass of A is MA, what must be the mass of B so that the value of g on B is half that of its value on A? Solve it.

Answer 1

Given:

Planet A:                            
 Mass=Ma 
 radius =Ra=Rb/2 -------------1
Planet B:
mass=Mb
radius =Rb

Condition given is : gb=1/2 ga------------2
From the relation :
g=Gm/R²
we have:
ga=GMa/RA²  -----------3
gb=GMb/Rb²    -------------4

substituting the equation 3 and 4 in equation 2 we get:

GMb/Rb²=1/2 [GMa/Ra²]
Mb/Rb²=1/2[Ma/Ra²]

since Ra=Rb/2
Mb/Rb²=1/2[ Ma/Rb²./4)
Mb/Rb²=4Ma/2xRb²
Ma/Rb²=2Ma/Rb2

∴Ma=2Mb

So, planet B needs to be double the mass of planet A in order to have gb=ga/2