Which one among the following statements is not correct?

Correct — B, Newton's law of gravitation follows from Newton's laws of motion. This is the false statement, and the reason is a matter of what each law is for. The three laws of motion are laws of dynamics: they tell you how a body behaves when a net force acts on it, whatever that force may be — electric, magnetic, frictional or gravitational. They contain no information about the strength or the form of any particular force. The law of gravitation is a separate, independent statement about one specific force: that every two masses attract along the line joining them with a force proportional to the product of the masses and inversely proportional to the square of their separation. You cannot obtain the second from the first. Historically Newton combined the second law with Kepler's observed planetary motions to argue that the attraction must fall off as the inverse square — but that is an inference from evidence, not a derivation from the laws of motion, and the gravitational constant G had to be measured, by Cavendish, more than a century later.

• (a)All bodies in the universe attract each other due to the gravitational force. — Correct as stated, so not the answer. Gravitation is universal — every pair of masses attracts, though for everyday objects the force is far too small to notice, which is why it is a negligible force at the atomic scale and the dominant one between celestial bodies.
• (c)The value of g (acceleration due to gravity) at the centre of the Earth is zero. — Correct as stated. At the centre the mass of the Earth surrounds you symmetrically in all directions; the pulls cancel exactly, so g falls to zero there. Note the contrast with pressure, which is at its maximum at the centre.
• (d)Mass and weight are measured in different units. — Correct as stated. Mass is the quantity of matter, measured in kilograms and unchanged wherever the body is taken; weight is the gravitational force on that mass, measured in newtons and different on the Moon from on the Earth.

Newton's three laws of motion define what a force does — the first establishes inertia and the concept of an unbalanced force, the second relates net force to the rate of change of momentum, and the third makes forces come in equal and opposite pairs. His law of universal gravitation is a distinct addition, giving the size of one particular force: F equals G m1 m2 divided by r squared. Taken together they explain both terrestrial fall and planetary orbit, which is why the pair is treated as a single achievement, but logically they remain independent.

A 'which is not correct' item on gravitation usually plants one statement that sounds like sound physics because it links two famous results. Test each option by asking what it would take to prove it. Universality, zero g at the centre and the unit distinction can each be argued directly. The claim in option (b) cannot: no manipulation of F equals ma yields an inverse-square law, because F equals ma holds for every force whatever its form. The same misconception shows up in other guises — that the third law explains why planets orbit, or that the second law predicts the value of g. It does not; g is measured, and its value depends on the Earth's mass and radius.

• Newton's law of universal gravitation states that every two masses attract with a force proportional to the product of the masses and inversely proportional to the square of the distance between them.
• The laws of motion describe how a body responds to a net force but say nothing about the origin or form of any particular force, so the law of gravitation does not follow from them.
• The gravitational constant G was measured experimentally by Cavendish, over a century after Newton published the law.
• At the centre of the Earth the surrounding mass pulls equally in every direction, so the acceleration due to gravity there is zero.
• Mass is measured in kilograms and is the same everywhere; weight is a force, measured in newtons, and varies with the local value of g.

• Assuming that because the laws of motion and the law of gravitation were published together they are logically dependent.
• Confusing g, the acceleration due to gravity at a place, with G, the universal gravitational constant.
• Thinking that gravity is strongest at the centre of the Earth; g is zero there, though pressure is greatest.

As a 'which statement is not correct' item mixing true statements about gravitation with one about the logical status of the law, or as a question on how g varies with depth and height.

• practice — not a real PYQ

  As one descends from the surface of the Earth towards its centre, the acceleration due to gravity does which one of the following?

  • (a)Increases steadily and is maximum at the centre
  • (b)Decreases and becomes zero at the centre
  • (c)Remains constant throughout
  • (d)First increases and then becomes infinite

  Answer(b) Decreases and becomes zero at the centre — the surrounding mass pulls equally in all directions there, so the net pull vanishes.

• practice — not a real PYQ

  Which one among the following pairs of physical quantity and SI unit is correctly matched?

  • (a)Mass — newton
  • (b)Weight — kilogram
  • (c)Weight — newton
  • (d)Acceleration due to gravity — newton per kilogram squared

  Answer(c) Weight — newton; weight is a force, while mass is measured in kilograms.