Question

A body hanging from a massless spring stretches it by 3 cm on earth's surface. At a place 800 km above the earth's surface, the same body will stretch the spring by (Radius of earth = 6400 km)

• A. $\frac{34}{27}$ cm
• B. $\frac{64}{27}$ cm
• C. $\frac{27}{64}$ cm
• D. $\frac{27}{34}$ cm
• E. $\frac{35}{81}$ cm

Hint:

Spring extension depends directly on weight, so it changes with gravity.

Answer 1

The Correct Option is B

Concept: Extension in spring: \[ x \propto g \] Gravitational acceleration varies as: \[ g' = g \left(\frac{R}{R+h}\right)^2 \]

Step 1: Given: \[ R = 6400, \quad h = 800 \] \[ R+h = 7200 \]

Step 2: Ratio of gravity: \[ \frac{g'}{g} = \left(\frac{6400}{7200}\right)^2 = \left(\frac{8}{9}\right)^2 = \frac{64}{81} \]

Step 3: New extension: \[ x' = x \cdot \frac{g'}{g} = 3 \times \frac{64}{81} \] \[ = \frac{192}{81} = \frac{64}{27} \] Final Answer: \[ \frac{64}{27} \text{ cm} \]