A negative work is done when an applied force F and the corresponding displacement S are
- (a)perpendicular to each other.
- (b)parallel to each other.
- (c)anti-parallel to each other.
- (d)equal in magnitude.
Correct — C, anti-parallel to each other. Work done is W = F·S·cosθ, where θ is the angle between the force F and the displacement S. The work is negative only when cosθ is negative, that is when θ lies between 90° and 180°. When the force and displacement are exactly anti-parallel, θ = 180° and cosθ = −1, so the work is maximally negative — the force acts directly against the motion, exactly as friction does on a sliding block.
- (a)perpendicular to each other. — At θ = 90°, cosθ = 0, so the work done is zero, not negative (for example, the centripetal force in circular motion).
- (b)parallel to each other. — At θ = 0°, cosθ = +1, giving maximum positive work — the force aids the motion, the opposite of negative work.
- (d)equal in magnitude. — The sign of work depends on the angle between force and displacement, not on whether their magnitudes are equal, so this says nothing about the work being negative.
Work done by a constant force is W = F·S·cosθ, the product of the force, the displacement, and the cosine of the angle between them. The sign of the work is fixed by cosθ: positive when the force has a component along the motion, zero when the force is perpendicular, and negative when the force opposes the motion.
To get negative work, cosθ must be negative, which needs θ greater than 90°. The extreme case is θ = 180° — force and displacement anti-parallel — giving the most negative work. Friction and the force of gravity on a body moving upward are everyday examples of forces doing negative work.
- Work done W = F·S·cosθ, where θ is the angle between force and displacement.
- θ = 0° (parallel) → maximum positive work; θ = 90° (perpendicular) → zero work.
- θ = 180° (anti-parallel) → cosθ = −1 → maximum negative work.
- Friction and gravity on a rising body are common sources of negative work.
Work is negative when the force opposes the displacement, i.e. when they are anti-parallel (θ = 180°), so the answer is (c).
- Confusing perpendicular (zero work) with anti-parallel (negative work).
- Thinking the magnitudes of F and S decide the sign; only the angle between them does.
Asked as the force–displacement orientation that gives negative work — identified from the sign of cosθ in W = F·S·cosθ.
No directly related past PYQ was found.
- practice — not a real PYQ
The work done by a force is zero when the angle between the force and the displacement is
- (a)0°
- (b)45°
- (c)90°
- (d)180°
Answer(c) 90° — cos 90° = 0, so W = F·S·cosθ = 0.
- practice — not a real PYQ
When a body is lifted vertically upward at constant speed, the work done by the force of gravity on it is
- (a)positive
- (b)negative
- (c)zero
- (d)infinite
Answer(b) negative — gravity acts downward while the displacement is upward (θ = 180°), so it does negative work.