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Question

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


A

Zero

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B

Infinite

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C

R times the weight of the object on the surface

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D

12R times the weight of the object on the surface

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Solution

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:

gd=g(1-dR) where gd 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:

gR=g(1-RR)gR=g×0gR=0

Hence, option A is correct.


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