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NEET 2023
Exam
NEET
Year
2023
Subject
Physics
Chapter
Gravitation

NEET 2023 · Physics · Gravitation

If R is the radius of the earth and g is the acceleration due to...

If RR is the radius of the earth and gg is the acceleration due to gravity on the earth surface. Then the mean density of the earth will be

Options

  1. A3g4πRG\frac{3 g}{4 \pi R G}
  2. B4πG3gR\frac{4 \pi G}{3 g R}
  3. CπRG12g\frac{\pi R G}{12 g}
  4. D3πR4gG\frac{3 \pi R}{4 g G}

Correct answer

A. 3g4πRG\frac{3 g}{4 \pi R G}

Step-by-step solution

Acceleration due to gravity on the earth surface g=GMR2g=\frac{G M}{R^2}g=G43πR3ρR2g=G43πRρ⇒ρ=3g4GπR\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}$$
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