Question

The weight of an object at the centre of the earth of radius R is
(a) zero
(b) infinite
(c) R times the weight at the surface of the earth
(d) 1/R2 times the weight at surface of the earth

Answer 1

(a) Zero
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The weight of an object at centre of the earth of radius R is zero.

Answer 2

The "weight of an object" at earth centre of 'radius R' is zero.

Answer - (Option A)

Explanation:

• The weight of an object is the force with that an object is attracted towards the earth centre.
• The weight (W) of a body is the "product of its mass" (m) and the "acceleration due to gravity".  

                                                     W = mg

• The "acceleration due to gravity" g at the earth centre is zero.  

                             $g^{\prime}=g\left(1-\frac{h}{R}\right)$

     When h is the distance from the earth’s surface to the earth’s centre and at the centre of the earth, h = R and $g^{\prime}$= 0

                        So, w = mg = m$\times$0 =0