Question

Planet $Y$ has density $D$, and surface gravitational acceleration, $g$. The radius of planet $Y$ is suddenly doubled while its density remains the same. Compared to the original $g$, the new value of the surface gravitational acceleration would be which of the following?

• A. $4g$
• B. $2g$
• C. $g$
• D. $g/2$

Answer 1

The correct option is B $2g$

Accelaration due to gravity $g=\frac{GM}{r^2}$
here $M=\frac{4}{3}\rho \pi r^3,\rho =D.$

So, $g=\frac{G\frac{4}{3}D\pi r^3}{r^2}=\frac{4}{3}GD\pi r......................\left(1\right)$.
Now, the radius is doubled with all the quantities kept constant.
New $g,g_n=\frac{4}{3}GD\pi \left(2r\right)=2g($from $\left(1\right))$