Assuming earth to be a sphere of uniform mass density, how much would a body weigh half way down the centre of the earth, if it weighed 100 N on the surface ?

Explanation

To solve the problem of how much a body would weigh halfway down to the center of the Earth, we can follow these steps:

### Step 1: Understand the Weight of the Body on the Surface
The weight of the body on the surface of the Earth is given as 100 N. This weight can be expressed using the formula:
\[ W = mg \]
where \( W \) is the weight, \( m \) is the mass of the body, and \( g \) is the acceleration due to gravity at the surface of the Earth.

### Step 2: Calculate the Mass of the Body
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