Question

The density of the earth is doubled keeping its radius constant then the acceleration due to gravity will be …………… $m{s}^{-2}(g=9.8m{s}^2)$

• A. $19.6$
• B. $9.8$
• C. $4.9$
• D. $2.45$

Answer 1

The correct option is A

$19.6$

Solution:

Step 1: Given data:

The density of the earth is doubled, and the mass will also be doubled, from the question,

$M\text{'}=2M$

Step 2: The formula of acceleration due to gravity will be,

$g=\frac{GM}{R^2}$

Now with the statement,

$$\begin{gathered} g\text{'}=\frac{G\left(2M\right)}{R^2} \\ g\text{'}=2g \\ g\text{'}=2\left(9.8\right) \\ g\text{'}=19.6m/s^2 \end{gathered}$$

Therefore the acceleration due to gravity will be $19.6$.

Hence, the correct option is (A).