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QAIPMT-2010-Ph-1970: NEET 2010 Physics - Class 11 AIPMT-2010-Ph-1970 Solution: The dependence of acceleration due to gravity g on the distance …
The dependence of acceleration due to gravity g on the distance r from the centre of the earth, assumed to be a sphere of radius R of uniform density is as shown in figures below. The correct figure is
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- A -4
- B -1
- C -2
- D -3
Step-by-Step Verified Solution
The acceleration due to gravity at a depth d below surface of earth is
g _ = G M R 2 ( 1 _ d R ) = g ( 1 _ d R )
g' = 0 at d = R.
i.e., acceleration due to gravity is zero at the centre of earth.
Thus, the variation in value g with r is
For, r > R,
g _ = g ( 1 + h R ) 2 = g R 2 r 2 _ g _ _ 1 r 2
Here, R + h = r
For r < R, g _ = g ( 1 _ d R ) = g r R
Here, R _ d = r _ g _ _ r
Therefore, the variation of g with distance from centre of the earth will be as shown in the figure.