-->

Motion In Straight Line

Question
CBSEENPH11017586

Why is a body is weightless at the center of the earth?

Solution

Weight of the body at any point, W = mg 
where,
g is the acceleration due to gravity at that point.
The acceleration due to gravity at a point inside the earth is, 
              straight g equals GM over straight R squared open parentheses 1 minus straight d over straight R close parentheses 
Therefore, 
Weight,  straight W space equals GMm over straight R squared open parentheses 1 minus straight d over straight R close parentheses 
At the center of the earth, d = R. 
So, straight W equals GMm over straight R squared open parentheses 1 minus straight R over straight R close parentheses equals 0
Thus, the body is weightless at the centre of the earth.