A body weighs $200 ext{ N}$ on the surface of the earth. How much will it weigh halfway down the centre of t

Question

A body weighs $200 	ext{ N}$ on the surface of the earth. How much will it weigh halfway down the centre of the earth?

Accepted Answer

1. **Formula for Gravity at Depth:** The acceleration due to gravity ($g_d$) at a depth $d$ below the surface of the Earth is given by the formula:
   $$ g_d = g \left( 1 - \frac{d}{R_E} ight) $$
   where $g$ is the acceleration due to gravity on the surface and $R_E$ is the radius of the Earth [Eq. 7.19].
2. **Given Data:**
   - Weight on surface, $W = mg = 200 	ext{ N}$.
   - Depth, $d = \frac{R_E}{2}$ (halfway to the centre).
3. **Calculation:**
   The new weight $W_d$ is $m g_d$.
   $$ W_d = m g \left( 1 - \frac{R_E/2}{R_E} ight) $$
   $$ W_d = W \left( 1 - \frac{1}{2} ight) $$
   $$ W_d = 200 \left( 0.5 ight) = 100 	ext{ N} $$

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