Question

The percentage decrease in the weight of a body when taken to a height of \(48\) km above the surface of the earth is (Radius of the earth is \(6400\) km)

• A. \(1\%\)
• B. \(1.5\%\)
• C. \(2\%\)
• D. \(2.5\%\)

Hint:

For small h, g falls by 2h/R.

Answer 1

The Correct Option is B

Step 1: Exact formula:
$g_h = g\left(\frac{R}{R+h}\right)^2 = g\left(\frac{6400}{6448}\right)^2$.

Step 2: Numbers:
$\frac{6400}{6448} = 0.99256$, and its square is $0.98518$. The decrease is $1 - 0.98518 = 0.0148$, about 1.5%.

Step 3: Cross-check:
The approximation $2h/R = 1.5\%$ agrees with the exact calculation, so option (B).

Final Answer:
The weight decreases by 1.5 percent, option (B). \[ \boxed{1.5\%} \]