Question

If the density of a planet is double than that of the earth and the radius is $1.5$ times that of the earth, the acceleration due to gravity on the surface of the planet is

• A. $\frac{3}{4}$ times that on the surface of earth
• B. $3$ times that on the surface of earth
• C. $\frac{4}{3}$ times that on the surface of earth
• D. $6$ times that on the surface of earth

Answer 1

The correct option is B $3$ times that on the surface of earth

Case 1: Earth

$Radius=r$

$Mass=M$

$Density=\rho$

$\therefore mg=G\frac{mM}{r^2}$

$mg=\frac{Gm}{r^2}\times \frac{4}{3}\pi r^3\rho$

$\therefore g=\frac{4\pi }{3}\left(Gr\rho \right)$

Case 2: Other palnet

$Radius=1.5r$

$Density=2\rho$

$\therefore m{g}^{\prime }=G\frac{m{M}^{\prime }}{(1.5r{)}^2}$

$m{g}^{\prime }=\frac{Gm}{2.25r^2}\times \frac{4}{3}\pi (1.5r{)}^3\times 2\rho$

$\therefore g^{\prime }=3g$