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  4. The gravitational field strength at the surface of a certain planet is g. Which of the following is the gravitational field strength at the surface of a planet with twice the radius and twice the mass?

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Q. The gravitational field strength at the surface of a certain planet is $g$. Which of the following is the gravitational field strength at the surface of a planet with twice the radius and twice the mass?

COMEDKCOMEDK 2015Gravitation

Solution:

For a given planet, $g = \frac{GM}{R^2}$
Gravitational field strength at the surface of another planet, $g' = \frac{GM'}{R'^2}$
Here, $M' = 2M , R' = 2R$
$\therefore \:\:\: g' = \frac{G(1M)}{(2R)^2} = \frac{g}{2}$