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JEE Main 2019 (10 Apr, Shift 1) · Acceleration Due to Gravity

Acceleration Due to Gravity question from JEE Main 2019 (10 Apr, Shift 1)

Q108JEE Main 2019 · 10 APR · SHIFT 1Easy

Acceleration Due to Gravity

The value of acceleration due to gravity at Earth's surface is 9.8 ms–2. The altitude above its surface at which the acceleration due to gravity decreases to 4.9 ms–2, is close to: (Radius of earth = 6.4 × 106 m)

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Answer: (d)

$g_h = \frac{g}{2}$ , so $\left(\frac{R}{R+h}\right)^2 = \frac{1}{2}$ .
$R + h = \sqrt{2}R \Rightarrow h = (\sqrt{2} - 1)R$
$h = 0.414 \times 6.4 \times 10^6 \approx 2.6 \times 10^6\ \text{m}$
So the answer is (d) $2.6 \times 10^6$ m.

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