Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g', then -
Answer & explanation
Correct answer: option 1
\(g = \frac{GM}{R^2} \)
\( g = G\frac{\frac{4}{3}\pi R^3 \rho}{R^2}\)
⇒ g = \(\frac{4}{3}\pi G \rho R\)
\(\Rightarrow g \propto R\)
\(\frac{g'}{g} = 3\)
\(g' = 3g\)