Question

If the radius of the earth is $R$,what is the weight of a body at the centre of the earth?

• A. $1/6$ times the weight at the surface ofthe earth
• B. $1/R^2$ times the weight at the surface of the earth
• C. Zero
• D. $4R$ times the weight at the surface of the earth

Answer 1

The correct option is C Zero

Answer is C.
The weight of an object is the maximum at the surface of the earth. As we move the body closer to the center of the earth, the mass of the earth between the center of the earth and the body keeps decreasing. This causes the force acting from the center of the earth on the body to decrease. Furthermore, the mass of earth above the body (between the body and the surface of the earth) keeps increasing as we move it further towards the center. So the forces acting on the body by this mass would slowly become more than the force acting on the body from the center of the earth. Finally, when you reach the center of the earth, the forces acting from all the directions would cancel each other out, and the body would experience no force.
Hence, the weight would be zero.