Question

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 new plant is g' then:

• A. g'= 3g
• B. g'= 9g
• C. $g^{\prime }=\frac{g}{9}$
  
• D. g'=27g

Answer 1

The correct option is A g'= 3g

$g=\frac{GM}{R^2}=\frac{G\left(Volumexdensity\right)}{R^2}=\frac{GV\rho }{R^2}\because V=\frac{4}{3}\pi R^3\Rightarrow g\propto R{g}^{\prime }=3g$