Question

A hypothetical planet has density $\rho$, radius R, and surface gravitational acceleration g. If the radius of the planet is doubled, but the planetary density stayed the same, the acceleration due to gravity at the planet’s surface would be

• A. $4g$
• B. $2g$
• C. $g$
• D. $\frac{g}{2}$

Answer 1

The correct option is B $2g$

Given that the density of the planet is $\rho$, and it has a radius R.
Acceleration due to gravity will be
$g=\frac{GM}{R^2}$
$=\frac{G\frac{4}{3}\pi R^3\rho }{R^2}$ [as mass = volume $\times$ density]
$=\frac{4}{3}\pi G\rho R$
Thus, we can say that $g\propto r$
Now since R is doubled, the new value of acceleration due to gravity will be twice the old value

Hence, the acceleration due to gravity will be $2g$