Question

the radius of planet A is half the radius of planet B if the mass of A is M suffix A what must be the mass of B so that the value of g on B is half that of its value on A?

Answer 1

mass of B=2 mass of A

Answer 2

The mass of B is double of Mass A.

Solution:

Let Radius of Planet A =$\mathrm{R}_{1}$

and Radius of Planet B = $\mathrm{R}_{2}$

Mass of Planet A =$\mathrm{M}_{1}$

and Mass of Planet B =$\mathrm{M}_{2}$

Therefore By the formula of gravity $\mathrm{g}=\frac{G M}{R^{2}}$

gravity of Planet A $= \mathrm{g}_{1}=\frac{G M_{1}}{R_{1}^{2}}$

and gravity of Planet B = $\mathrm{g}_{2}=\frac{G M_{2}}{R_{2}^{2}}$

given that Radius of planet A is half of planet B

Hence $R_{1}=\frac{R_{2}}{2} ,$

and value of g on B is half than value of g on A

that is,

$g_{2}=2 g_{1}$

$\frac{E M_{2}}{R_{2}^{2}}=\frac{G M_{1}}{R_{1}^{2}}$

$\frac{M_{2}}{R_{2}^{2}}=\frac{2 M_{1}}{\left(\frac{R_{2}}{2}\right)^{2}}$

$M_{2}=2 M_{1}$

Hence Mass of B is double of Mass A.