Chapter 7.1, Problem 10SSC

To determine

Effect on gravitational acceleration $g$ on the earth’s surface.

Answer to Problem 10SSC

Gravitational acceleration $g$ will increase.

Explanation of Solution

Given:

Earth shrinks i.e. $R$ is decreased

Mass of earth is constant.

Formula used:

The gravitational force can be obtained by:

  $F=\frac{Gm{m}_E}{R^2}$

Here,

  $F$ is force of gravity

  $G$ is gravitational constant

  $m$ is mass of object

  $m_E$ is mass of earth

  $R$ is radius of earth

Also, $F=mg$

  $g$ is acceleration due to gravity

Calculation:

As, $F=\frac{Gm{m}_E}{R^2}$

So,

  $\begin{array}{l}mg=\frac{Gm{m}_E}{R^2}\\ g=\frac{G{m}_E}{R^2}\end{array}$

Since $G$ is constant and $m_E$ is also given constant and $R$ is decreasing

Hence, $g$ will be inversely proportional to $R$ i.e. $g$ will increase.