ECAT — Engineering College Admission Test (UET)

ECAT Physics — Measurements, Vectors and Equilibrium (Set 3)

Take the ECAT Physics — Measurements, Vectors and Equilibrium (Set 3): 30 multiple-choice questions (40 minutes) with instant scoring and a full answer…

What this test covers

30 ECAT Physics

Sample questions with answers

The first 5 questions of this test, with the correct answer and explanation.

Q1. The dimensions of pressure are
- A. [ML⁻²T⁻²]
- B. [ML²T⁻²]
- C. [ML⁻¹T⁻²] ✓
- D. [MLT⁻²]
Answer: C. [ML⁻¹T⁻²]
Explanation: Pressure = force/area = [MLT⁻²]/[L²] = [ML⁻¹T⁻²].
Q2. How many significant figures are there in the number 0.004050?
- A. 4 ✓
- B. 6
- C. 3
- D. 5
Answer: A. 4
Explanation: Leading zeros are not significant; 4, 0, 5 and the trailing 0 after the decimal point are, giving 4.
Q3. A car moves at 72 km/h. Its speed in SI units is
- A. 40 m/s
- B. 72 m/s
- C. 7.2 m/s
- D. 20 m/s ✓
Answer: D. 20 m/s
Explanation: 72 × 1000 m / 3600 s = 20 m/s.
Q4. The side of a cube is measured with a percentage uncertainty of 2%. The percentage uncertainty in its volume is
- A. 6% ✓
- B. 8%
- C. 4%
- D. 2%
Answer: A. 6%
Explanation: V = a³, so ΔV/V = 3 Δa/a = 3 × 2% = 6%.
Q5. The mass of a body is (50.0 ± 0.5) g and its volume is (10.0 ± 0.2) cm³. The percentage uncertainty in its density is
- A. 2%
- B. 3% ✓
- C. 1%
- D. 1.5%
Answer: B. 3%
Explanation: Δρ/ρ = Δm/m + ΔV/V = 1% + 2% = 3%.

The other 25 questions

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Q6. For A = 2i + 3j − k and B = i − 2j + 4k, the scalar product A·B is
- A. -2
- B. -8
- C. 8
- D. -14
Q7. The angle between the vectors 2i + 2j and 3i is
- A. 90°
- B. 60°
- C. 30°
- D. 45°
Q8. The area of the triangle whose adjacent sides are the vectors 2i + j and i + 3j is
- A. 5 square units
- B. 2.5 square units
- C. 3.5 square units
- D. 7 square units
Q9. Two forces of 7 N and 8 N act at a point with an angle of 60° between them. The magnitude of the resultant is
- A. 11 N
- B. 13 N
- C. √113 N
- D. 15 N
Q10. Which of the following cannot be the magnitude of the resultant of a 5 N and a 12 N force?
- A. 20 N
- B. 17 N
- C. 13 N
- D. 7 N
Q11. The component of a 100 N force along the vertical, when the force makes 30° with the horizontal, is
- A. 25 N
- B. 86.6 N
- C. 50 N
- D. 100 N
Q12. A 60 N weight hangs from the midpoint of a light string whose two halves each make 30° with the horizontal. The tension in each half is
- A. 60 N
- B. 30 N
- C. 120 N
- D. 52 N
Q13. A force of 20 N acts on a spanner 0.5 m long at 30° to the spanner. The torque about the nut is
- A. 10 N m
- B. 20 N m
- C. 5 N m
- D. 8.7 N m
Q14. A child of mass 40 kg sits 1.5 m from the pivot of a light see-saw. Where must a child of mass 30 kg sit on the other side to balance it?
- A. 1.0 m
- B. 2.0 m
- C. 2.5 m
- D. 1.5 m
Q15. A uniform beam 4 m long weighing 200 N rests on supports at its two ends. A 600 N load is placed 1 m from the left end. The reaction at the right support is
- A. 200 N
- B. 250 N
- C. 400 N
- D. 350 N
Q16. A uniform ladder 5 m long weighing 200 N leans against a smooth vertical wall with its foot 3 m from the wall on rough ground. The friction force at the ground is
- A. 50 N
- B. 100 N
- C. 150 N
- D. 75 N
Q17. The dimensions of the universal gravitational constant G are
- A. [M⁻¹L²T⁻²]
- B. [ML³T⁻²]
- C. [M⁻¹L³T⁻¹]
- D. [M⁻¹L³T⁻²]
Q18. Planck's constant h is defined by E = hf. Its dimensions are
- A. [ML²T⁻¹]
- B. [MLT⁻¹]
- C. [ML⁻²T]
- D. [ML²T⁻²]
Q19. Centripetal force is assumed to depend on m, v and r as F = k mᵃ vᵇ rᶜ. Dimensional analysis gives c equal to
- A. 2
- B. 1
- C. −1
- D. −2
Q20. On a vernier callipers 10 vernier divisions coincide with 9 main-scale divisions, each of 1 mm. The least count is
- A. 0.9 mm
- B. 1 mm
- C. 0.1 mm
- D. 0.01 mm
Q21. A screw gauge has pitch 0.5 mm and 50 circular divisions. Its reading shows 2.5 mm on the linear scale and 27 on the circular scale, with a zero error of +0.03 mm. The true diameter is
- A. 2.70 mm
- B. 2.74 mm
- C. 2.76 mm
- D. 2.80 mm
Q22. The sum 12.11 + 18.0 + 1.013 should be reported, with the correct number of significant digits, as
- A. 31.12
- B. 31.1
- C. 31
- D. 31.123
Q23. A heater uses 2 kW h of electrical energy. Expressed in joules this is
- A. 1.2 × 10⁵ J
- B. 2 × 10⁶ J
- C. 7.2 × 10³ J
- D. 7.2 × 10⁶ J
Q24. The unit vector along A = 3i − 4j + 12k is
- A. (3i − 4j + 12k)/√19
- B. (3i − 4j + 12k)/5
- C. (3i − 4j + 12k)/13
- D. (3i − 4j + 12k)/19
Q25. A quantity x = a b³/c is calculated from measurements with percentage uncertainties 1% in a, 2% in b and 3% in c. The percentage uncertainty in x is
- A. 10%
- B. 6%
- C. 4%
- D. 12%
Q26. If A = 2i + 3j and B = 4i + 6j, the magnitude of A × B is
- A. 24
- B. √13
- C. 0
- D. 12
Q27. A force F = 3i + 4j newtons displaces a body by d = 2i − j metres. The work done is
- A. 2 J
- B. 6 J
- C. 10 J
- D. −2 J
Q28. A body is acted on by a 6 N force due north and an 8 N force due east. A third force that keeps it in equilibrium has magnitude
- A. 10 N
- B. 2 N
- C. 7 N
- D. 14 N
Q29. Two equal and opposite parallel forces of 15 N each act along lines 0.4 m apart. The torque of this couple is
- A. 0 N m
- B. 37.5 N m
- C. 6 N m
- D. 12 N m
Q30. A ball resting on a horizontal table is in which state of equilibrium?
- A. Dynamic
- B. Neutral
- C. Unstable
- D. Stable