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 — B, 1 cm. The spring's extension is proportional to the stretching force, which is the weight mg (Hooke's law: mg = kx). On the Moon g is one-sixth of Earth's, so the weight and hence the extension become one-sixth: 6 cm / 6 = 1 cm.
- (a)6 cm — That would be true only if the weight were unchanged; but on the Moon the weight (mg) is smaller because g is one-sixth, so the extension shrinks.
- (c)0 cm — Gravity on the Moon is weaker but not zero, so the spring still stretches — by 1 cm, not zero.
- (d)36 cm — This multiplies by six instead of dividing; weaker Moon gravity reduces the extension, it does not increase it.
A hanging spring stretches until its restoring force balances the weight: kx = mg, so x = mg/k. The mass m and the spring constant k are unchanged when you move to the Moon, but g falls to one-sixth, so the extension x falls to one-sixth as well.
Key idea: extension depends on WEIGHT (mg), not mass alone. Moon g = g/6 means x(Moon) = x(Earth)/6 = 6/6 = 1 cm. The '6 cm' trap forgets that weight changes; '36 cm' scales the wrong way.
- Hooke's law: kx = mg, so extension x = mg/k.
- Mass and spring constant do not change on the Moon.
- Moon's gravity is one-sixth of Earth's.
- Extension on the Moon = 6 cm / 6 = 1 cm.
- Confusing mass (unchanged) with weight (which changes with g).
- Scaling the extension up instead of down for weaker gravity.
Asked as the change in spring extension or spring-balance reading between Earth and the Moon.
No directly related past PYQ was found.
- practice — not a real PYQ
A spring balance reads 60 N for an object on Earth. On the Moon it would read
- (a)60 N
- (b)10 N
- (c)360 N
- (d)0 N
Answer(b) 10 N (weight is one-sixth).
- practice — not a real PYQ
A hanging spring stretches by x under weight mg. If g halves, the extension becomes
- (a)2x
- (b)x/2
- (c)x
- (d)0
Answer(b) x/2.