1. Use the variation of gravity with height

   Weight is proportional to gravitational acceleration, so at height $h$ above Earth: $g_h = g\left(\frac{R}{R+h}\right)^2$ where:

   • $R = 6400\,\text{km}$
   • $h = 32\,\text{km}$

2. Find the ratio of new weight to original weight

   Since $W \propto g$, $\frac{W_h}{W} = \left(\frac{R}{R+h}\right)^2 = \left(\frac{6400}{6400+32}\right)^2$ $= \left(\frac{6400}{6432}\right)^2$

3. Use approximation for small heights

   For $h \ll R$, $\frac{\Delta g}{g} \approx \frac{2h}{R}$ Hence percentage decrease in weight: $\frac{\Delta W}{W} \times 100 \approx \frac{2h}{R} \times 100$

   Substituting values: $\frac{\Delta W}{W} \times 100 = \frac{2\times 32}{6400} \times 100$ $= \frac{64}{6400} \times 100$ $= 0.01 \times 100 = 1\%$

4. Check with exact calculation

   $\left(\frac{6400}{6432}\right)^2 \approx (0.9950)^2 \approx 0.990\,,$ so decrease is about: $1 - 0.990 = 0.010 = 1\%$

5. Evaluate options

   • A: $1\%$ ✅
   • B: $3\%$ ❌
   • C: $4\%$ ❌
   • D: $0.5\%$ ❌

Therefore, the correct answer is A.