Question

Two planets have same density but different radii.The accelaration due to gravity would be

• A. same on both planets
• B. greater on the planet with smaller radius
• C. greater on the planet with larger radius
• D. depending on the distance of planet from the Sun

Answer 1

The correct option is C greater on the planet with larger radius

Accelaration due to gravity on the surface of a planet is $$g=\frac{GM}{R^2}...\left(1\right)$$Where $M$ is the mass of planet and $R$ is the radius of the planet.

Also, $M=\rho V=\frac{4}{3}\pi R^3\rho$

Substituting it equation $\left(1\right)$, we get

$g=\frac{G}{R^2}\times \left(\frac{4}{3}\pi G{R}^3\rho \right)$

$\therefore g=\frac{4}{3}\pi GR\rho$

Thus, $g\propto R$

So, acceleration due to gravity would be greater on a planet with larger radius.

Key Concept: Acceleration due to gravity on the surface of a planet is given by $$g=\frac{GM}{R^2}$$