Directions : The following two (2) items consist of two statements, Statement I and Statement II. Examine these two statements carefully and select the correct answer using the code given below. Code : (a) Both the statements are individually true and Statement II is the correct explanation of Statement I (b) Both the statements are individually true but Statement II is not the correct explanation of Statement I (c) Statement I is true but Statement II is false (d) Statement I is false but Statement II is true Statement I : The force on Moon due to Earth is the action, while the force on Earth due to Moon is the reaction. Statement II : To every action, there is an equal and opposite reaction.

Correct — A, (a) Both the statements are individually true and Statement II is the correct explanation of Statement I. This is the first of the two items governed by the Directions block printed above it, and that block is worth reading before anything else because its four-way code decides how the item is answered.

Statement II is Newton’s third law of motion, stated in Newton’s own crisp form: to every action there is always an equal and opposite reaction. It is a fundamental law of mechanics and it is true.

Statement I applies that law to the Earth and the Moon. The Earth attracts the Moon gravitationally; the Moon attracts the Earth gravitationally; the two forces are equal in magnitude, opposite in direction, act along the line joining the two bodies, and arise from one and the same interaction. Newton’s law of gravitation gives both of them by the same expression, so their magnitudes cannot differ. They are therefore a genuine action-reaction pair, and calling the force on the Moon the action and the force on the Earth the reaction is a correct description of that pair. The labelling is a matter of convention rather than of physics — the textbook is explicit that any one of the two may be called action and the other reaction, and that no cause-and-effect order is implied, since the two forces act at the same instant — but a convention correctly applied is not an error, and Statement I is true.

And Statement II explains Statement I. Statement I asserts that two particular forces stand in the action-reaction relation; the only thing that makes that assertion true is the general law in Statement II, which says that forces always occur in such pairs. Remove the third law and there is no reason at all why the Moon should pull back on the Earth. That is the test the code’s first two branches ask you to apply: not whether both statements are about the same topic, but whether the second is the reason the first is true. Here it is, so the answer is option (a).

One feature of the code deserves attention because it is a live tool on both this item and the next. There are only four branches, and none of them is ’both statements are false’. At least one statement is therefore true on each of these two questions. Since Statement II here is a bare statement of a fundamental law, it is certainly the true one, which eliminates option (c) before Statement I has even been considered.

Why the others are wrong

• (b)Both the statements are individually true but Statement II is not the correct explanation of Statement I — This branch is for the case where two true statements sit side by side without one explaining the other — a genuine possibility in this format, and the reason the format exists. It does not fit here. Statement I is not an independent fact that happens to coexist with the third law; it is an instance of the third law, and the third law is the whole of its justification. A useful way to test the explanation limb is to ask whether the first statement would still be true if the second were false. If the mutual forces between two bodies were not always equal and opposite, there would be no action-reaction pair between Earth and Moon to describe, and Statement I would collapse. That dependence is exactly what ’correct explanation’ means.
• (c)Statement I is true but Statement II is false — This says the third law is false, which no examiner intends and no physics supports. It is the branch a candidate reaches when he has misread the code and matched ’Statement II is false’ to a suspicion about Statement I instead. Read the four branches carefully: (c) and (d) each condemn one specific statement, and here neither statement is false. It may also be tempting to think the third law fails for gravity because the two bodies never touch, but the law is not a law about contact — the textbook uses the Earth and a falling stone as its own example of a non-contact action-reaction pair, noting that the stone does exert an equal and opposite force on the Earth, which we simply never notice because the Earth is so massive.
• (d)Statement I is false but Statement II is true — This says Statement I is false, and the objection a thoughtful candidate has in mind when he chooses it is a real one: which force is called the action and which the reaction is arbitrary, so how can Statement I be stated as a fact? The answer is that Statement I is not claiming that the force on the Moon must be called the action; it is naming one force as the action and the other as the reaction, which is exactly what the convention permits. The pair is real, the labels are free, and applying free labels in one of the two permitted ways does not make the statement false. A second and more common route to this option is the belief that the Earth pulls the Moon harder than the Moon pulls the Earth. It does not. The forces are equal; what is unequal is the acceleration each produces, because acceleration is force divided by mass and the Earth is about eighty-one times as massive as the Moon.

Newton’s third law says that forces come in pairs: whenever body B exerts a force on body A, body A exerts a force on body B, equal in magnitude and opposite in direction. In symbols, the force on A by B equals minus the force on B by A. Three features of the law cause almost all the confusion around it. First, the two forces act on different bodies, so they never cancel each other; adding them up and concluding that nothing can accelerate is the classic error. If, on the other hand, the two bodies are treated as a single system, the pair becomes an internal force pair and does cancel, which is why internal forces drop out when the second law is applied to a system of particles. Second, there is no cause and effect between them: they act at the same instant, neither precedes the other, and either may be called the action. Third, the law holds for forces at a distance as well as for contact forces. Gravitation is the standard illustration. Newton’s law of gravitation gives the mutual attraction between two masses by a single expression, so the Earth-Moon force and the Moon-Earth force are necessarily equal in magnitude and opposite in direction, and together they are what keeps the Moon in orbit while making the Earth itself wobble slightly about the common centre of mass of the two bodies. The unequal effects come from the second law, not the third: the same force produces a much larger acceleration in the lighter body.

Key facts

• Newton’s third law, in Newton’s own wording: to every action there is always an equal and opposite reaction.
• Action and reaction act on different bodies and therefore never cancel; treated as one system, they become internal forces and do cancel.
• There is no cause-and-effect order between action and reaction; they act at the same instant, and either may be called the action.
• The third law applies to forces at a distance as well as to contact forces; the Earth and a falling stone are the textbook example.
• Newton’s law of gravitation gives the mutual force between two masses by a single expression, so the Earth-Moon and Moon-Earth forces are necessarily equal in magnitude.
• The Earth is about eighty-one times as massive as the Moon, so the same magnitude of force accelerates the Moon far more than it accelerates the Earth.
• The Directions block over this item governs Q91 and Q92 only, and its code has no branch for both statements being false.

Common traps

• Choosing branch (a) whenever both statements are true. The branch also requires that the second explains the first.
• Believing that the heavier body exerts the larger force. The forces are equal; the accelerations differ.
• Adding an action-reaction pair together and concluding the net force is zero. They act on different bodies.
• Thinking the third law needs contact. It holds for gravitational and electrostatic forces too.
• Overlooking that this code has no both-false branch, and so missing an elimination that is free.

• practice — not a real PYQ

  A book lies at rest on a table. Which of the following is the reaction to the weight of the book, in the sense of Newton’s third law?

  • (a)The normal force exerted on the book by the table
  • (b)The gravitational force exerted on the Earth by the book
  • (c)The weight of the table
  • (d)The force of friction between the book and the table

  Answer(b) The gravitational force exerted on the Earth by the book

• practice — not a real PYQ

  Two bodies of unequal mass attract each other gravitationally. Which of the following is correct?

  • (a)The heavier body exerts the greater force and undergoes the greater acceleration
  • (b)The heavier body exerts the greater force but undergoes the smaller acceleration
  • (c)Both bodies experience forces of equal magnitude, and the lighter body undergoes the greater acceleration
  • (d)Both bodies experience forces of equal magnitude and equal accelerations

  Answer(c) Both bodies experience forces of equal magnitude, and the lighter body undergoes the greater acceleration