Question

The radius of planet A is half of the radius of planet B if the mass of a easy Ma what must be the mass of be so that the value of g on B of half that of its value on

Answer 1

let, radius of planet A = Ra
radius of planet B = Rb

g on planet A = ga
g on planet B = gb

given Ra=Rb/2
and gb= ga/2

we know ,

g∝M/R²

therefore , ga/gb = (Ma/Ra²)/(Mb/Rb²)
=> ga/(ga/2) = {Ma/(Rb/2)²}/(Mb/Rb²)
=> 2=4Ma/Mb
=>Mb=2Ma

Answer 2

let, radius of planet A = Raradius of planet B = Rb
g on planet A = gag on planet B = gb
given Ra=Rb/2and gb= ga/2
we know ,
g∝M/R²
therefore , ga/gb = (Ma/Ra²)/(Mb/Rb²)=> ga/(ga/2) = {Ma/(Rb/2)²}/(Mb/Rb²)=> 2=4Ma/Mb=>Mb=2Ma