An object weighs 9 N on the surface of the Earth. What would be its weight, when measured on the surface of a planet where the acceleration due to gravity is 9 times that on the surface of the Earth ?
- (a)The weight would remain the same
- (b)The weight would be equal to 1 N
- (c)The weight would become 9 times
- (d)The weight will be reduced to 1⁄9 N
Correct — C, The weight would become 9 times. Weight is the force gravity exerts on a body, W = mg, so it is the product of two things — the mass of the body, which travels with it and does not change, and the local acceleration due to gravity, which belongs to the planet. Moving the object to a planet where g is nine times the Earth's value leaves m untouched and multiplies g by nine, so the weight is multiplied by nine as well: 9 N becomes 81 N. The mass, meanwhile, stays at about 0·92 kg wherever the object goes, because 9 N divided by roughly 9·8 m/s² is what it was on Earth and nothing about a journey changes the amount of matter in a body.
- (a)The weight would remain the same — True of the mass, not of the weight. Mass is the constant; weight is the force gravity applies to that mass, and it changes from one planet to another exactly as g does.
- (b)The weight would be equal to 1 N — Divides by nine instead of multiplying. It also fails a common-sense check — stronger gravity has to pull harder, so the weight cannot come out smaller than it was on Earth.
- (d)The weight will be reduced to 1⁄9 N — The same division carried a step further, and wrong in the same direction. On a planet with nine times the Earth's gravity an object is pulled nine times as hard, not ninety times more gently.
Mass measures the quantity of matter in a body and is the same everywhere; it is measured in kilograms. Weight is the gravitational force acting on that mass, W = mg, measured in newtons, and it depends on where the body is. On the Earth's surface g is about 9·8 m/s²; on the Moon it is about one-sixth of that, so an astronaut's weight falls to a sixth while the mass is unaltered. At the centre of the Earth g is zero and so is weight, and in free fall inside an orbiting spacecraft the sensation of weight disappears altogether even though gravity is still acting.
The item is a one-line substitution, and the only thing standing between a candidate and the mark is the habit of using 'weight' where 'mass' is meant. Reading the stem strictly — an object WEIGHS 9 N, and the planet's g is nine times the Earth's — leaves only one operation to perform. A direction check catches the two wrong answers before any arithmetic: a stronger pull must give a larger force. It is also worth carrying the actual numbers, since they make the distinction concrete. On Earth the object has a mass of about 0·92 kg and a weight of 9 N; on the new planet the mass is still 0·92 kg and the weight is 81 N.
- Weight W = mg, measured in newtons; mass m is measured in kilograms and is the same everywhere.
- On Earth g is about 9·8 m/s², so a 9 N object has a mass of roughly 0·92 kg.
- Where g is nine times the Earth's value, that same object weighs 81 N — nine times as much.
- On the Moon g is about one-sixth of the Earth's, so weight falls to a sixth while mass is unchanged.
- Weight is zero at the centre of the Earth and is not felt in free fall, although mass is unaffected in both cases.
Mass is carried by the body, weight is supplied by the planet — which is the whole content of the question.
- Treating weight as a fixed property of the object and answering that it stays the same.
- Dividing by the factor instead of multiplying, so that stronger gravity produces a smaller weight.
- Quoting a weight in kilograms, which are units of mass.
As a change-of-planet calculation like this one, or by comparing readings on a spring balance and a beam balance taken at the same place.
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
Answer(b) 1 cm
The identical relation run the other way. A spring stretches in proportion to the weight hung on it, so dividing g by six divides the extension by six — just as multiplying g by nine here multiplies the weight by nine.
The acceleration due to gravity at the Earth's surface depends on
- (a) its mass only.
- (b) its radius only.
- (c) both its mass and radius.
- (d) either its mass or its radius.
Answer(c) both its mass and radius.
Where the multiplying factor in this question comes from. A planet's g follows from its own mass and radius, which is why a different planet can have nine times the Earth's value and multiply every weight on its surface accordingly.
- practice — not a real PYQ
A body has a mass of 60 kg on the Earth. On the Moon, where g is one-sixth of its value on the Earth, the mass of the body will be
- (a)10 kg
- (b)60 kg
- (c)360 kg
- (d)6 kg
Answer(b) 60 kg — mass is the quantity of matter and does not change with location; it is the weight that falls to one-sixth.
- practice — not a real PYQ
A spring balance and a beam balance are both taken to the Moon and used to compare an object with a standard. Which one of the following will give the same reading as on the Earth?
- (a)The spring balance only
- (b)The beam balance only
- (c)Both of them
- (d)Neither of them
Answer(b) The beam balance only — it compares two masses, and gravity acts equally on both pans; a spring balance responds to weight, which has changed.