1. Use the formula for gravity at height

At a height $h$ above Earth's surface,

$g_h = g\left(\frac{R}{R+h}\right)^2$

where:

• $g = 9.8\,\text{m s}^{-2}$ at the surface,
• $g_h = 4.9\,\text{m s}^{-2}$,
• $R = 6.4 \times 10^6\,\text{m}$.

2. Substitute the given values

$4.9 = 9.8\left(\frac{R}{R+h}\right)^2$

Divide both sides by $9.8$:

$\frac{4.9}{9.8} = \left(\frac{R}{R+h}\right)^2$

$\frac{1}{2} = \left(\frac{R}{R+h}\right)^2$

3. Take square root

$\frac{R}{R+h} = \frac{1}{\sqrt{2}}$

So,

$R+h = \sqrt{2}\,R$

$h = (\sqrt{2}-1)R$

4. Put $R = 6.4 \times 10^6\,\text{m}$

$h = (1.414 - 1)(6.4 \times 10^6)$

$h = 0.414 \times 6.4 \times 10^6$

$h \approx 2.65 \times 10^6\,\text{m}$

5. Match with the options

$h \approx 2.6 \times 10^6\,\text{m}$

So the correct option is D.

6. Option check

• A: $1.6 \times 10^6$ m — incorrect
• B: $9.0 \times 10^6$ m — incorrect
• C: $6.4 \times 10^6$ m — incorrect
• D: $2.6 \times 10^6$ m — correct