Question

Suppose a planet exists whose mass and radius both are half that of the earth The acceleration due to gravity on the surface of this planet will be double ?

Answer 1

As we know that the acceleration in earth is calculated by the formula $\frac{Gm}{r^2}$ which equals $9.8m/s^2$ where m is the mass of the earth and r is the radius of the earth.

now,

mass of that planet is half of earth so it's mass is $\frac{1}{2}\left(m\right)$ and it's radius is half of earth so, it's radius is $\frac{1}{2}\left(r\right)$

we will use the same formula to find the gravitational acceleration of that planet which equals

$\frac{G\left(\frac{1}{2}\right)m}{\left(\frac{1}{2}\right)r^2}=\frac{\frac{Gm}{2}}{\frac{r^2}{4}}=\frac{2Gm}{r^2}\ast 2$

now, substitute for $\frac{Gm}{r^2}$ of earth

$=9.8\times 2=19.6m/s^2$

so, the value of g on that planet will be $19.6m/s^2$