Question

The acceleration due to gravity on the surface of earth is g. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be:

• A. g/4
• B. 4g
• C. g/2
• D. 2g

Answer 1

The Correct Option is B

To address the problem, it is necessary to determine how the acceleration due to gravity, represented by \(g\), is influenced by the Earth's dimensions and mass. The formula for gravitational acceleration at a planet's surface is:

\(g = \frac{G \cdot M}{R^2}\)

where:

• \(G\) denotes the gravitational constant.
• \(M\) represents the Earth's mass.
• \(R\) signifies the Earth's radius.

The problem states that the Earth's diameter is halved, implying its radius is also halved. Consequently, the new radius is calculated as \(R_{new} = \frac{R}{2}\).

Given that the Earth's mass remains constant, we can substitute \(R_{new}\) into the gravitational acceleration formula:

\(g_{new} = \frac{G \cdot M}{(R_{new})^2} = \frac{G \cdot M}{(\frac{R}{2})^2}\)

This expression simplifies to:

\(g_{new} = \frac{G \cdot M}{\frac{R^2}{4}} = \frac{4 \cdot G \cdot M}{R^2}\)

The above calculation indicates that the new acceleration due to gravity is:

\(g_{new} = 4g\)

Therefore, if the Earth's diameter is reduced by half while its mass is held constant, the surface acceleration due to gravity will be \(4g\). The correct answer is: 4g.