JEE Main 2026 — Apr 5, Shift 1 — Physics solution

JEE Main2026Apr 5, Shift 1Physics

When one moves from a point 16 km below the earth's surface to a point 16 km above the earth's surface. The change in $g$ is approximately $α$ %. The value of $α$ is _______.

(Take radius of the earth $= 6400$ km.)

A
0.12
B
0.25
C
0.50
D
0.75

Solution

For small $h ≪ R$ , the standard approximations give

$g_{above} \approx g (1 - \frac{2 h}{R})$ , $g_{below} \approx g (1 - \frac{h}{R})$ .

So $Δ g = g_{below} - g_{above} = \frac{g h}{R}$ , and

$\frac{Δ g}{g} \times 100 = \frac{h}{R} \times 100 = \frac{16}{6400} \times 100 = 0.25%$ .

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