Question

What is the percentage decrease in the weight of a body when it is taken to a height of 32 km from the surface of earth?
(Given: \( R = 6400 \, \text{km} \))

• A. 1.5%
• B. 1%
• C. 2%
• D. 0.5%

Hint:

For small heights compared to earth’s radius, always use the approximation \[ \frac{\Delta W}{W} = \frac{2h}{R}. \] It saves time in numerical problems.

Answer 1

The Correct Option is B

Step 1: Relation between weight and height.
The weight of a body at height \( h \) above the earth’s surface is given by:
\[ W_h = W \left( \frac{R}{R+h} \right)^2 \] where \( R \) is the radius of earth.
Step 2: Percentage decrease in weight.
The fractional decrease in weight is approximately:
\[ \frac{\Delta W}{W} = \frac{2h}{R} \] when \( h \ll R \).
Step 3: Substituting values.
\[ \frac{\Delta W}{W} = \frac{2 \times 32}{6400} = \frac{64}{6400} = 0.01 \]
Step 4: Converting to percentage.
\[ 0.01 \times 100 = 1% \]
Step 5: Conclusion.
The percentage decrease in weight is 1%.