Level 1 — RecognitionWork, Energy & Power

Work, Energy & Power

⏱ 20 minutes30 marksprintable — key stays hidden on paper

Level 1: Recognition (MCQ + Matching + True/False with Justification)

Time Limit: 20 minutes Total Marks: 30

Section A — Multiple Choice (1 mark each) [10 marks]

Choose the single best answer.

Q1. The work done by a force $\vec{F}$ acting on a body during displacement $\vec{d}$ is: (a) $\vec{F} \times \vec{d}$ (b) $\vec{F} \cdot \vec{d}$ (c) $|\vec{F}||\vec{d}|$ (d) $\frac{\vec{F}}{\vec{d}}$

Q2. The SI unit of power is the watt, which equals: (a) $\text{J}\cdot\text{s}$ (b) $\text{J/s}$ (c) $\text{N}\cdot\text{m}$ (d) $\text{kg}\cdot\text{m/s}$

Q3. A force acts perpendicular to the displacement of an object. The work done is: (a) maximum (b) negative (c) zero (d) equal to $Fd$

Q4. The elastic potential energy stored in a spring stretched by $x$ is: (a) $kx$ (b) $\frac{1}{2}kx^2$ (c) $-kx$ (d) $\frac{1}{2}kx$

Q5. The work–energy theorem states that the net work done on a body equals its: (a) change in momentum (b) change in potential energy (c) change in kinetic energy (d) total mechanical energy

Q6. For a variable force $F(x)$ , the work done from $x_1$ to $x_2$ is: (a) $F(x_2 - x_1)$ (b) $\int_{x_1}^{x_2} F\,dx$ (c) $\frac{dF}{dx}$ (d) $F \cdot x$

Q7. Which of the following is a non-conservative force? (a) gravity (b) spring force (c) friction (d) electrostatic force

Q8. Kinetic energy of a body of mass $m$ moving with speed $v$ is: (a) $mv$ (b) $\frac{1}{2}mv^2$ (c) $mv^2$ (d) $\frac{1}{2}mv$

Q9. The efficiency of a machine is defined as: (a) $\frac{\text{input}}{\text{output}}$ (b) $\frac{\text{useful output}}{\text{input}}$ (c) input − output (d) input × output

Q10. Hooke's law for a spring is expressed as: (a) $F = kx$ (b) $F = -kx$ (c) $F = \frac{1}{2}kx^2$ (d) $F = -\frac{1}{2}kx$

Section B — Matching (1 mark each) [6 marks]

Q11. Match Column I with Column II.

Column I	Column II
(i) Gravitational PE (near Earth)	(P) $\frac{1}{2}kx^2$
(ii) Spring PE	(Q) $\frac{1}{2}mv^2$
(iii) Kinetic energy	(R) $mgh$
(iv) Gravitational PE (general)	(S) $-\dfrac{GMm}{r}$
(v) Instantaneous power	(T) $\vec{F}\cdot\vec{v}$
(vi) Average power	(U) $\dfrac{W}{t}$

Section C — True/False with Justification (2 marks each) [14 marks]

State True or False (1 mark) and give a one-line justification (1 mark).

Q12. Work done by a conservative force around any closed path is zero.

Q13. Friction always does negative work on a moving block.

Q14. If the net work done on a body is zero, its speed does not change.

Q15. The joule and the watt are the same unit.

Q16. For a spring, the restoring force is directed opposite to the displacement.

Q17. Mechanical energy is conserved even when non-conservative forces do net work.

Q18. A machine can have efficiency greater than 100%.

Answer keyMark scheme & solutions

Section A — MCQ (1 mark each)

Q1. (b) $\vec{F}\cdot\vec{d}$ — Work is the scalar (dot) product of force and displacement. [1]

Q2. (b) J/s — Power is energy per unit time; $1\text{ W} = 1\text{ J/s}$ . [1]

Q3. (c) zero — $W = Fd\cos 90^\circ = 0$ ; perpendicular force does no work. [1]

Q4. (b) $\frac{1}{2}kx^2$ — obtained from $\int_0^x kx\,dx$ . [1]

Q5. (c) change in kinetic energy — $W_{net} = \Delta KE$ . [1]

Q6. (b) $\int_{x_1}^{x_2}F\,dx$ — work of a variable force is the integral of force over displacement. [1]

Q7. (c) friction — friction is dissipative and path-dependent. [1]

Q8. (b) $\frac{1}{2}mv^2$ — standard KE formula. [1]

Q9. (b) useful output / input — ratio of useful energy out to energy in. [1]

Q10. (b) $F = -kx$ — restoring force opposes displacement (negative sign). [1]

Section B — Matching (1 mark each)

Q11. (i) → (R) $mgh$ (ii) → (P) $\frac{1}{2}kx^2$ (iii) → (Q) $\frac{1}{2}mv^2$ (iv) → (S) $-\frac{GMm}{r}$ (v) → (T) $\vec{F}\cdot\vec{v}$ (vi) → (U) $W/t$ [6 total — 1 per correct pair]

Section C — True/False with Justification (2 marks each)

Q12. True. By definition a conservative force does path-independent work, so net work over a closed loop is zero. [T=1, reason=1]

Q13. False. Friction opposes relative motion but can do positive work (e.g. on a block carried by a moving conveyor/plank where static friction acts in the direction of motion). [F=1, reason=1]

Q14. False. Zero net work means $\Delta KE = 0$ , so speed is unchanged — but the statement as phrased is actually True: zero net work ⇒ constant kinetic energy ⇒ constant speed. Accept True, justification: $W_{net}=\Delta KE=0 \Rightarrow v$ constant. [T=1, reason=1]

Q15. False. Joule measures energy; watt measures power (energy/time). They differ dimensionally. [F=1, reason=1]

Q16. True. $F=-kx$ ; the negative sign shows the restoring force is opposite to the displacement. [T=1, reason=1]

Q17. False. Mechanical energy is conserved only when net non-conservative work is zero; friction/drag dissipate it. [F=1, reason=1]

Q18. False. Output cannot exceed input (energy conservation); efficiency $\le 100\%$ . [F=1, reason=1]

[
  {"claim": "Spring PE from integral of kx equals 1/2 k x^2", "code": "k,x=symbols('k x',positive=True); W=integrate(k*x,(x,0,x)); result = simplify(W - Rational(1,2)*k*x**2)==0"},
  {"claim": "Work at 90 degrees is zero", "code": "F,d=symbols('F d',positive=True); W=F*d*cos(pi/2); result = simplify(W)==0"},
  {"claim": "Kinetic energy from work-energy theorem: integral of m*a over dx gives 1/2 m v^2", "code": "m,v=symbols('m v',positive=True); KE=integrate(m*v,(v,0,v)); result = simplify(KE - Rational(1,2)*m*v**2)==0"},
  {"claim": "Zero net work implies KE unchanged", "code": "dKE=symbols('dKE'); Wnet=0; result = (Eq(Wnet,dKE).subs(dKE,0))==True or solve(Eq(Wnet,dKE),dKE)[0]==0"}
]