Level 1 — RecognitionMeasurement, Vectors & Kinematics

Measurement, Vectors & Kinematics

⏱ 20 minutes25 marksprintable — key stays hidden on paper

Level 1 Paper — Recognition

Time limit: 20 minutes Total marks: 25

Section A — Multiple Choice Questions (1 mark each)

Choose the single best option.

Q1. Which of the following is a fundamental (base) SI quantity? (a) Force (b) Electric current (c) Velocity (d) Energy

Q2. The SI unit of the derived quantity pressure is: (a) $\text{N·m}$ (b) $\text{kg·m/s}^2$ (c) $\text{N/m}^2$ (d) $\text{kg·m}^2/\text{s}^2$

Q3. The dimensional formula of force is: (a) $[MLT^{-1}]$ (b) $[MLT^{-2}]$ (c) $[ML^2T^{-2}]$ (d) $[ML^{-1}T^{-2}]$

Q4. The number $0.00450$ has how many significant figures? (a) 2 (b) 3 (c) 4 (d) 5

Q5. A zero-error in a screwgauge that always adds $0.02$ mm to every reading is an example of: (a) Random error (b) Systematic error (c) Least-count error (d) Gross mistake

Q6. Which of the following is a vector quantity? (a) Speed (b) Mass (c) Displacement (d) Temperature

Q7. For two vectors $\vec{A}$ and $\vec{B}$ with angle $\theta$ between them, $\vec{A}\cdot\vec{B}$ equals: (a) $AB\sin\theta$ (b) $AB\cos\theta$ (c) $AB\tan\theta$ (d) $A/B\cos\theta$

Q8. The magnitude of $\vec{A}\times\vec{B}$ is maximum when $\theta$ equals: (a) $0^\circ$ (b) $45^\circ$ (c) $90^\circ$ (d) $180^\circ$

Q9. A body thrown vertically upward at its highest point has: (a) $v=0,\ a=0$ (b) $v=0,\ a=g$ downward (c) $v\ne0,\ a=0$ (d) $v=g,\ a=0$

Q10. The unit vector along $\vec{A}=3\hat{i}+4\hat{j}$ is: (a) $3\hat{i}+4\hat{j}$ (b) $\frac{3\hat{i}+4\hat{j}}{5}$ (c) $\frac{3\hat{i}+4\hat{j}}{7}$ (d) $\frac{3\hat{i}+4\hat{j}}{25}$

Q11. In projectile motion (no air resistance), the horizontal component of velocity is: (a) Constant (b) Increasing (c) Decreasing (d) Zero at top

Q12. The slope of a position–time graph gives: (a) Acceleration (b) Displacement (c) Velocity (d) Distance

Section B — Matching (1 mark each pair, 5 marks)

Q13. Match Column I with Column II:

Column I	Column II
(i) Area under $v$ – $t$ graph	(P) Acceleration
(ii) Slope of $v$ – $t$ graph	(Q) Displacement
(iii) Work done	(R) $\vec{r}\times\vec{F}$
(iv) Torque	(S) $\vec{F}\cdot\vec{d}$
(v) Range of projectile	(T) $\dfrac{u^2\sin 2\theta}{g}$

Section C — True/False with justification (2 marks each: 1 verdict + 1 reason)

Q14. Adding a scalar to a vector is a valid physical operation.

Q15. Two physical quantities having the same dimensions must be the same physical quantity.

Q16. The result of $2.5\ \text{m} \times 3.42\ \text{m}$ should be reported as $8.6\ \text{m}^2$ .

Q17. For a boat crossing a river, the resultant velocity relative to ground is the vector sum of the boat's velocity relative to water and the river's velocity.

Q18. During free fall, taking upward as positive, the acceleration of a ball moving downward is negative.

Answer keyMark scheme & solutions

Section A (1 mark each)

Q1 — (b) Electric current. Why: The seven SI base quantities are length, mass, time, current, temperature, amount, luminous intensity. Force/velocity/energy are derived. (1)

Q2 — (c) $\text{N/m}^2$ . Why: Pressure = force/area $= \text{N/m}^2 = \text{Pa}$ . (1)

Q3 — (b) $[MLT^{-2}]$ . Why: $F=ma$ , so $[M][LT^{-2}]=[MLT^{-2}]$ . (1)

Q4 — (b) 3. Why: Leading zeros are not significant; digits 4, 5, and trailing 0 after decimal count → 4,5,0. (1)

Q5 — (b) Systematic error. Why: A constant reproducible offset (zero error) is systematic, not random. (1)

Q6 — (c) Displacement. Why: It has both magnitude and direction; speed, mass, temperature are scalars. (1)

Q7 — (b) $AB\cos\theta$ . Why: Definition of the dot (scalar) product. (1)

Q8 — (c) $90^\circ$ . Why: $|\vec{A}\times\vec{B}|=AB\sin\theta$ , maximum when $\sin\theta=1$ . (1)

Q9 — (b) $v=0,\ a=g$ downward. Why: Velocity vanishes at top but gravity still acts. (1)

Q10 — (b) $\frac{3\hat{i}+4\hat{j}}{5}$ . Why: $|\vec{A}|=\sqrt{9+16}=5$ ; unit vector $=\vec{A}/|\vec{A}|$ . (1)

Q11 — (a) Constant. Why: No horizontal acceleration ⇒ $v_x$ unchanged. (1)

Q12 — (c) Velocity. Why: Slope of $x$ – $t$ = $dx/dt$ = velocity. (1)

Q13 (1 mark per correct match): (i)→(Q) area under $v$ – $t$ = displacement; (ii)→(P) slope of $v$ – $t$ = acceleration; (iii)→(S) $W=\vec{F}\cdot\vec{d}$ ; (iv)→(R) $\vec{\tau}=\vec{r}\times\vec{F}$ ; (v)→(T) $R=\frac{u^2\sin 2\theta}{g}$ . (5)

Section C (1 verdict + 1 reason)

Q14 — FALSE. Why: Scalars and vectors are different mathematical objects; only like quantities may be added. Scalar + vector is undefined. (2)

Q15 — FALSE. Why: Same dimensions ≠ same quantity, e.g. work and torque both $[ML^2T^{-2}]$ but are physically distinct. (2)

Q16 — TRUE. Why: $2.5\times3.42 = 8.55$ ; the least significant-figure factor (2.5) has 2 s.f., so result rounds to $8.6\ \text{m}^2$ . (2)

Q17 — TRUE. Why: Galilean velocity addition: $\vec{v}_{bg}=\vec{v}_{bw}+\vec{v}_{wg}$ . (2)

Q18 — FALSE. Why: With upward positive, $g$ acceleration is $-9.8\ \text{m/s}^2$ regardless of motion direction; but the statement's reasoning ("because moving downward") is wrong — acceleration is negative always, not because of motion direction. Verdict FALSE for the causal claim; acceleration sign is fixed by convention, independent of velocity direction. (2)

[
  {"claim":"Magnitude of 3i+4j is 5","code":"result = (sqrt(3**2+4**2)==5)"},
  {"claim":"Force dimension MLT^-2 from F=ma","code":"M,L,T=symbols('M L T'); F=M*(L/T**2); result = (F==M*L*T**-2)"},
  {"claim":"2.5*3.42 rounds to 8.6 (2 sig figs)","code":"result = (round(2.5*3.42,1)==8.6)"},
  {"claim":"Range formula gives u^2 sin(2*theta)/g","code":"u,theta,g=symbols('u theta g'); R=u**2*sin(2*theta)/g; result = simplify(R - u**2*2*sin(theta)*cos(theta)/g)==0"}
]