The force with which the Earth attracts an object is called:

Correct — A, Weight of the object. Weight is by definition the force with which the Earth attracts a body, and since it is a force it is measured in newtons and calculated as mass times the acceleration due to gravity, W equals mg. Everything follows from that. Weight is a vector, directed towards the centre of the Earth. It changes with place, because g changes: a body weighs slightly more at the poles than at the equator, less on a mountain top, and about one-sixth as much on the Moon. Mass, by contrast, does not change at all — it is the amount of matter in the body and the measure of its inertia, and a 50 kilogram body is a 50 kilogram body on the Earth, on the Moon or in orbit. The everyday habit of saying we 'weigh 50 kilograms' blurs the two, but the physics keeps them strictly apart.

• (b)Mass of the object — Mass is the quantity of matter in a body and the measure of its inertia, in kilograms. It is a scalar, it is the same everywhere in the universe, and it is not a force.
• (c)Density of the object — Density is mass per unit volume, in kilograms per cubic metre. It describes how tightly matter is packed and says nothing about the Earth's pull on the body.
• (d)Magnitude of the object — Not a physical quantity. 'Magnitude' means the size of a quantity — one speaks of the magnitude of a force or of a velocity, never of an object.

By the law of universal gravitation the Earth attracts every body with a force equal to G M m divided by R squared, where M and R are the Earth's mass and radius. Collecting the constants into a single quantity g, the acceleration due to gravity, of about 9.8 metres per second squared at the surface, that force becomes simply mg — and it is this force that is called the weight of the body. Weight and mass are therefore related but distinct: the second is an intrinsic property of the body, the first is what a particular gravitational field does to it.

Definition questions of this kind reward the discipline of attaching a unit to every term before choosing. Weight is in newtons, mass in kilograms, density in kilograms per cubic metre; only the first is a unit of force, and the stem asks for a force. The distinction has real consequences worth remembering. A spring balance measures weight and so reads differently on the Moon; a beam balance compares masses and reads the same. An astronaut in orbit is weightless not because gravity has disappeared but because the spacecraft and everything in it are in continuous free fall, so nothing presses on anything else — the mass is entirely unchanged.

• Weight is the force with which the Earth attracts a body, W = mg, and is measured in newtons.
• Mass is the quantity of matter in a body, is measured in kilograms and is the same everywhere.
• Weight is a vector directed towards the centre of the Earth; mass is a scalar.
• Because g varies with latitude and altitude, weight varies from place to place, and a body weighs about one-sixth as much on the Moon as on the Earth.
• A spring balance measures weight while a beam balance compares masses, which is why only the first gives a different reading on the Moon.

• Using kilograms for weight in ordinary speech and then repeating that in an examination.
• Assuming that weightlessness in orbit means gravity is absent; the spacecraft is in free fall.
• Confusing density with weight — a body may be heavy and yet less dense than another that is lighter.

As a one-line definition item, as a units-matching question, or as a comparison of the readings of a spring balance and a beam balance in different gravitational fields.

• practice — not a real PYQ

  The SI unit in which the weight of a body is expressed is which one of the following?

  • (a)Kilogram
  • (b)Newton
  • (c)Joule
  • (d)Pascal

  Answer(b) Newton — weight is a force, W = mg; the kilogram is the unit of mass.

• practice — not a real PYQ

  A body is taken from the Earth to the Moon. Which one of the following statements is correct?

  • (a)Both its mass and its weight decrease
  • (b)Its mass remains the same but its weight decreases
  • (c)Its mass decreases but its weight remains the same
  • (d)Both its mass and its weight remain the same

  Answer(b) Its mass remains the same but its weight decreases — mass is intrinsic, while weight depends on the local value of g, which on the Moon is about one-sixth of the Earth's.