Question

If the density of the earth is doubled keeping its radius constant then the acceleration due to gravity ( present value 9.8m/s²) will be

• A. $2.45$ m/s²
• B. $4.9$m/s²
• C. $9.8$m/s²
• D. $19.6$ mls²

Answer 1

The correct option is D

$19.6$ mls²

Step 1 :Given

The density of the earth is doubled.

The radius of earth kept constant

Step-2:Formula

We know that,

$Density=\frac{Mass}{Volume}$

$D=\frac{M}{V}$, Where D is density, M is mass, and V is volume.

1. If the volume is the same and the density of the earth is doubled, then the earth's mass is also doubled.
2. So, the mass will be doubled. It means that M in the above equation will be replaced by 2M.
3. Finally, the value of Acceleration due to gravity(g) will be doubled.

$2D=\frac{2M}{V}$

Step 3: Finding g when mass is doubled:

The value of $g=$$\frac{GM}{R^2}$

But the mass is doubled,

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

$$\begin{gathered} g=9.8m/s^2 \\ g=\left(2\right)\times 9.8 \\ =19.6m/s^2 \end{gathered}$$

Hence, the correct option is (d). Now, the value of acceleration due to gravity will be $19.6m{s}^{-2}$