JEE Main · 2022 · 26 Jun 2022 · Shift 1 · Gravitation

The variation of acceleration due to gravity (g) with distance (

r

) from the center of the earth is correctly represented by : (Given

R =

radius of earth)

(A)(see structure)
✓ Correct
(B)(see structure)
(C)(see structure)
(D)(see structure)

Answer: (A)

Solution

For

r \leq R

(inside Earth):

g = \frac{GM r}{R ^{3}}

, which is linear in r. For

r \geq R

(outside Earth):

g = \frac{GM}{r ^{2}}

, which decreases as

1/ r^{2}

. At

r = R

, both expressions give

g = \frac{GM}{R ^{2}}

. The correct graph shows a linear increase from 0 to R, then a

1/ r^{2}

decrease beyond R.

JEE Main · 2022 · 26 Jun 2022 · Shift 1 · Single correct option

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