Enforcement Officer / Accounts Officer (EO/AO) 2020 recruitment test, advertisement 421. Transcribed from the Commission's own booklet (series A, NMJX-U-GTA); answer as per the official UPSC final answer key. This question is in Part B. Answer last reviewed 24 August 2026.

Which one of the following statements regarding force is correct ?

(a)A positive force implies attractive nature.
(b)A negative force implies repulsive nature.
(c)A positive force can be both attractive and repulsive in nature.
(d)A negative force implies attractive nature.

Answer

Why

Correct — D, (d) A negative force implies attractive nature. When the force between two particles is written as a single signed quantity, the sign is measured along the line joining them with the OUTWARD direction — the direction of increasing separation — taken as positive. A force that pushes the particles apart therefore comes out positive, and a force that pulls them together comes out negative. The two standard laws show it at once. Coulomb's law gives F = k q1 q2 / r^2: for like charges the product q1 q2 is positive, the force is positive, and the charges repel; for unlike charges the product is negative, the force is negative, and they attract. Newton's law of gravitation is written F = -G m1 m2 / r^2, carrying a minus sign permanently, because gravitation between masses is always attractive. The same convention appears in the relation between force and potential energy, F = -dU/dr: a potential energy that rises with separation, as in a bound system, gives a negative force pulling the particles back together. So negative and attractive go together, which is what this option states.

Why the others are wrong

(a)A positive force implies attractive nature. — This reverses the convention. Positive means directed along increasing separation, which is a push outward — repulsion, not attraction. The option is attractive in a loose everyday way, because 'positive' sounds like drawing together and 'negative' like driving apart, and that verbal intuition is exactly the opposite of the physics. The check that settles it in one line is Coulomb's law with two like charges: q1 q2 is positive, so F is positive, and two like charges plainly repel each other.
(b)A negative force implies repulsive nature. — This is the same reversal as the previous option, stated from the other end, and the two of them together are simply the wrong convention written twice. Under the standard convention a negative force acts towards decreasing separation, which is a pull inward. The clearest single counter-example is gravitation, which is universally attractive and is written with a leading minus sign for precisely that reason; if a negative force implied repulsion, the gravitational force between the Earth and a falling stone would push the stone away.
(c)A positive force can be both attractive and repulsive in nature. — If this were true the sign would carry no information at all, and there would be no point in writing it. The whole purpose of the convention is that the sign of the force along the line joining two particles tells you the DIRECTION in which it acts, and therefore whether the interaction is attractive or repulsive. A positive value means outward and so repulsive; it cannot simultaneously mean inward. The option seems designed for a candidate who half-remembers that a force is a vector whose sign depends on the axis chosen, and concludes that the sign is arbitrary. The choice of axis is a convention, but once the outward direction is fixed as positive — which is the standard choice for a two-body interaction — each sign has exactly one meaning.

Concept

Force is a vector, so a single number can describe it only when a direction has already been agreed. For the interaction between two particles the agreed direction is radial: draw the line joining them and call the outward sense, the sense of increasing separation r, positive. With that fixed, a positive force pushes them apart (repulsive) and a negative force draws them together (attractive). The convention runs through the whole of mechanics and electrostatics. Coulomb's law F = k q1 q2 / r^2 delivers the sign automatically from the product of the charges — like charges repel, unlike attract — while Newton's law of gravitation carries an explicit minus sign because gravitation admits only one possibility. The link to energy is the deeper statement: for a conservative force, F = -dU/dr, so the force always points down the slope of the potential energy curve, towards lower potential energy. In a bound system such as an electron in an atom or a planet in orbit, the potential energy is negative and rises towards zero as the separation grows, so the slope dU/dr is positive and the force is negative — attractive, holding the system together. That is why bound states are described as having negative total energy, and why the energy needed to separate the parts to infinity is called the binding energy. Reading a potential energy graph is the same skill: where the curve rises the force is attractive, where it falls the force is repulsive, and where it is flat, at a minimum, the force is zero and the system is in equilibrium — which is how the equilibrium bond length of a molecule is defined.

This is a convention question rather than a computation, and general ability papers use conventions to separate candidates who have used the physics from those who have only read about it. Every option is a short sentence of the same shape, so nothing can be eliminated on grounds of form; the only route through is to know which way the sign points, or to reconstruct it from a law you remember. Reconstructing is the reliable method, and the fastest reconstruction is the gravitational one — gravity is always attractive and is always written with a minus sign.

Key facts

For a two-particle interaction the outward radial direction, that of increasing separation, is taken as positive.
A positive force is repulsive; a negative force is attractive.
Coulomb's law, F = k q1 q2 / r^2, yields a positive force for like charges (repulsion) and a negative force for unlike charges (attraction).
Newton's law of gravitation is written with a leading minus sign because gravitational force is always attractive.
For a conservative force, F = -dU/dr: the force points towards decreasing potential energy.
In a bound system the potential energy is negative and total energy is negative; the energy required to separate the parts to infinity is the binding energy.
On a potential energy curve, a rising section corresponds to an attractive force, a falling section to a repulsive force, and a minimum to zero force and stable equilibrium.
Force is a vector; a bare sign describes it only after a positive direction has been fixed.

The sign is measured outward, so negative means pulling inward

(d) A negative force implies attractive nature — CORRECT→When the force between two particles is written as a single signed quantity, the sign is measured along the line joining them, with the OUTWARD direction — that of increasing separation — taken as positive. A force that draws the particles together therefore comes out negative.

(a) A positive force implies attractive nature — FALSE→This reverses the convention. Positive means directed along increasing separation, which is a push outward: repulsion. The option is tempting in a loose everyday way, because ‘positive’ sounds like drawing together and ‘negative’ like driving apart — and that verbal intuition is exactly the opposite of the physics.

(b) A negative force implies repulsive nature — FALSE→The same reversal stated from the other end; the two wrong options together are simply the wrong convention written twice. The clearest single counter-example is gravitation, which is universally attractive and is written with a leading minus sign for precisely that reason.

(c) A positive force can be both — FALSE→If this were true the sign would carry no information at all, and there would be no point in writing it. The whole purpose of the convention is that the sign tells you the direction in which the force acts along the line joining the particles, and therefore whether the interaction attracts or repels.

The two laws that show it→Coulomb’s law, F = k q1 q2 / r^2, delivers the sign automatically from the product of the charges: like charges give a positive product, a positive force and repulsion; unlike charges give a negative product, a negative force and attraction. Newton’s law of gravitation, F = -G m1 m2 / r^2, carries the minus sign permanently, because gravitation admits only one possibility.

The deeper statement — force against potential energy→For a conservative force, F = -dU/dr, so the force always points down the slope of the potential energy curve, towards lower potential energy. In a bound system the potential energy is negative and rises towards zero as separation grows, so the slope is positive and the force is negative — attractive, holding the system together. On a potential-energy graph a rising section means an attractive force, a falling section a repulsive one, and a minimum means zero force and stable equilibrium.

Study next

Newton's three laws of motion and the vector nature of forceCoulomb's law and the electrostatic force between point chargesNewton's law of universal gravitation, and gravitational field and potentialConservative and non-conservative forces, potential energy, and the relation F = -dU/drPotential energy curves, equilibrium positions and binding energyThe four fundamental forces of nature and their relative strengths and ranges

Common traps

Letting the everyday sense of 'positive' as welcoming and 'negative' as repelling decide the answer. The physics runs the other way.
Concluding that because a sign depends on the choice of axis, it can mean anything. For a two-body interaction the outward direction is the standard positive direction.
Forgetting that gravitation is written with a minus sign because it is always attractive — the quickest check available.
Confusing the sign of the FORCE with the sign of the potential ENERGY. Both are negative for a bound attractive system, but they are different quantities.
Assuming the sign of the charges alone settles it in Coulomb's law without checking the product. Two negative charges give a positive product and repel.

Physics items on EO/AO papers that carry no numbers are usually convention or definition items of this kind, offered as four one-line statements of which exactly one is correctly worded. The recurring subjects are force and its sign, scalar versus vector quantities, the distinction between mass and weight, and units. The distractors are typically the same statement with a term swapped, so the productive method is to fix the correct version in your head first and then find the option that matches it rather than judging each option on its own.

Related PYQs

EPFO_EOAO_2020_Q46Open & attempt →

Which one of the following statements is true with regard to the image formation by two eyes of a person ?

(a) Both the eyes see exactly the same image.
(b) One eye sees half portion of the object.
(c) Both the eyes combine the two images seen by them.
(d) Each eye sees a slightly different image.

Answer(d) Each eye sees a slightly different image.

The other four-statement item in this physics block. Both are decided by which sentence states the physics correctly rather than by any calculation, and in both the wrong options are the correct idea with one term reversed or misplaced.

Practice

practice — not a real PYQ
The electrostatic force between two point charges is found to be negative. This means that the charges are
- (a)both positive
- (b)both negative
- (c)of opposite sign, and the force is attractive
- (d)of opposite sign, and the force is repulsive
Answer(c) of opposite sign, and the force is attractive
practice — not a real PYQ
For a conservative force acting along a line, the relation between the force F and the potential energy U is
- (a)F = dU/dr
- (b)F = -dU/dr
- (c)F = U x r
- (d)F = -U/r
Answer(b) F = -dU/dr

Why