Q114 / 200 · NEET 2023 (Manipur) · Physics

If $R$ is the radius of the earth and $g$ is the acceleration due to gravity on the earth surface. Then the mean density of the earth will be

  • Correct answer
    A
    $\frac{3 g}{4 \pi R G}$
  • B
    $\frac{4 \pi G}{3 g R}$
  • C
    $\frac{\pi R G}{12 g}$
  • D
    $\frac{3 \pi R}{4 g G}$

Solution

Acceleration due to gravity on the earth surface $g=\frac{G M}{R^2}$ $\begin{aligned} & \frac{g=G \frac{4}{3} \pi R^3 \rho}{R^2} \\ & g=G \frac{4}{3} \pi R \rho \\ & \Rightarrow \rho=\frac{3 g}{4 G \pi R}\end{aligned}$

Hence, the correct answer is option: 'A'.

More Gravitation Questions