JEE Main · 2022 · 28 Jul 2022 · Shift 1 · Gravitation

If the radius of earth shrinks by

2%

while its mass remains same. The acceleration due to gravity on the earth's surface will approximately :

(A)decrease by $2%$
(B)decrease by $4%$
(C)increase by $2%$
(D)increase by $4%$ ✓ Correct

Answer: (D)

Solution

Acceleration due to gravity is

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

. Since

M

is constant,

g \propto \frac{1}{R ^{2}}

. Taking differentials:

\frac{Δ g}{g} = - 2 \frac{Δ R}{R}

. Given

\frac{Δ R}{R} = - 2%

(shrinkage), we have

\frac{Δ g}{g} = - 2 \times (- 2%) = + 4%

. Thus

g

increases by 4%.

JEE Main · 2022 · 28 Jul 2022 · Shift 1 · Single correct option

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