Question

If the density of earth is doubled keeping its radius constant, then acceleration due to gravity g is

• A. 20 m/s\(^2\)
• B. 10 m/s\(^2\)
• C. 5 m/s\(^2\)
• D. 2.5 m/s\(^2\)

Hint:

\(g = GM/R^2 = \frac{4}{3}\pi G \rho R\).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
\(g = \frac{4}{3}\pi G R \rho\), so \(g \propto \rho\) when R constant.
Step 2: Detailed Explanation:
\(g \propto\) density
New \(g = 2 \times 10 = 20\ \mathrm{m/s^2}\)
Step 3: Final Answer:
New g is \(20\ \mathrm{m/s^2}\).