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 :
- A.6 cm
- B.1 cm
- C.0 cm
- D.36 cm
Correct answer
Explanation
The correct answer is B, 1 cm. The stretch of a spring is proportional to the force on it, and the weight of the mass on the Moon is one-sixth of its weight on Earth.
By Hooke's law, the extension x of a spring equals F/k, where k is the spring constant. Here the stretching force is the weight of the hanging mass, mg. The mass m and the spring constant k stay the same on the Moon; only g falls to one-sixth. So the force, and with it the extension, becomes one-sixth of 6 cm, that is 1 cm. This is also why a spring balance shows a smaller reading on the Moon while a beam balance, which compares two masses, shows the same.
A is wrong because it treats weight as if it did not depend on gravity. C is wrong because the Moon does have gravity, so the mass still has weight. D is wrong because it multiplies by six instead of dividing.
Exam tip: mass is the same everywhere, weight changes with g; a spring balance measures weight, a beam balance compares mass.
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