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: Understanding the Concept:
Weight is \(mg\), so the fractional change in weight equals the fractional change in \(g\). At a height \(h\) much smaller than \(R\):
\[ g_h \approx g\left(1 - \frac{2h}{R}\right) \]

Step 2: Compute:
\[ \frac{\Delta g}{g} = \frac{2h}{R} = \frac{2\times48}{6400} = \frac{96}{6400} = 0.015 \]

Step 3: Percentage:
\(0.015 \times 100 = 1.5\%\). The weight decreases by 1.5%.

Step 4: Why the other options are wrong.
1% would result from using \(h/R\) without the 2 and a different height. 2% and 2.5% are too large for \(h = 48\) km.

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