Question

The weight of an object at the center of the earth of radius $R$ is

• A. Zero
• B. Infinite
• C. R times the weight of the object on the surface
• D. $\frac{1}{2R}$ times the weight of the object on the surface

Answer 1

The correct option is A

Zero

Step 1: Given:

The object is at the center of the earth

Thus, $d=R$ where $d$ is the depth of the object from the surface and $R$ is the radius of the earth

Step 2: Formula used:

$g_d=g(1-\frac{d}{R})$ where $g_d$ is the acceleration due to gravity at depth $d$ and $g$ is the acceleration due to gravity at the surface

$W=mg$ where $W$ is the weight of the object

Step 3: Calculating the weight at the center:

$$\begin{gathered} g_R=g(1-\frac{R}{R}) \\ {g}_R=g\times 0 \\ {g}_R=0 \end{gathered}$$

Hence, option A is correct.