A mass is attached to a spring that hangs vertically. The extension produced in the spring is 6 cm on Earth. The acceleration due to gravity on the surface of the Moon is one-sixth of its value on the surface of the Earth. The extension of the spring on the Moon would be :

The extension of a vertical spring is governed by Hooke’s Law and the weight of the attached mass. The relationship is expressed as F = kx, where F is the force, k is the spring constant, and x is the extension.

In this scenario, the force is the weight of the mass (W = mg). Therefore, the extension is calculated as: x = mg / k.

• Since the mass (m) and the spring constant (k) are intrinsic properties that do not change, the extension (x) is directly proportional to the acceleration due to gravity (g).
• The acceleration due to gravity on the Moon is 1/6th of its value on Earth (gmoon = gearth / 6).
• Applying this ratio: Extension on Moon = (1/6) × Extension on Earth = (1/6) × 6 cm = 1 cm.

Thus, Option B is the correct answer.