ECAT — Engineering College Admission Test (UET)

ECAT Physics — Measurements, Vectors and Equilibrium (Set 2)

Take the ECAT Physics — Measurements, Vectors and Equilibrium (Set 2): 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. Which one of the following is NOT an SI base unit?
- A. mole
- B. kelvin
- C. candela
- D. newton ✓
Answer: D. newton
Explanation: The seven SI base units are metre, kilogram, second, ampere, kelvin, mole and candela; the newton (kg m s⁻²) is a derived unit.
Q2. Stokes' law gives the drag on a sphere as F = 6πηrv. What are the dimensions of the coefficient of viscosity η?
- A. [ML⁻¹T⁻²]
- B. [ML⁻¹T⁻¹] ✓
- C. [ML⁻²T⁻¹]
- D. [MLT⁻¹]
Answer: B. [ML⁻¹T⁻¹]
Explanation: η = F/(6πrv) = [MLT⁻²]/([L][LT⁻¹]) = [ML⁻¹T⁻¹].
Q3. Surface tension is defined as force per unit length. What are its dimensions?
- A. [ML⁻¹T⁻²]
- B. [MLT⁻²]
- C. [MT⁻²] ✓
- D. [ML²T⁻²]
Answer: C. [MT⁻²]
Explanation: [MLT⁻²]/[L] = [MT⁻²].
Q4. The speed v of transverse waves on a string is assumed to depend on the tension T and the mass per unit length μ as v ∝ Tᵃμᵇ. Dimensional analysis gives:
- A. a = −½, b = ½
- B. a = ½, b = −½ ✓
- C. a = 1, b = −1
- D. a = ½, b = ½
Answer: B. a = ½, b = −½
Explanation: [LT⁻¹] = [MLT⁻²]ᵃ[ML⁻¹]ᵇ: M: a + b = 0, T: −2a = −1 so a = ½ and b = −½, i.e. v ∝ √(T/μ).
Q5. A Wi-Fi router transmits at 5 GHz. Expressed in hertz, this frequency is:
- A. 5 × 10³ Hz
- B. 5 × 10¹² Hz
- C. 5 × 10⁶ Hz
- D. 5 × 10⁹ Hz ✓
Answer: D. 5 × 10⁹ Hz
Explanation: The prefix giga (G) means 10⁹, so 5 GHz = 5 × 10⁹ Hz.

The other 25 questions

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Q6. Two lengths are measured as 20.5 ± 0.2 cm and 12.3 ± 0.1 cm. What is their difference, with its uncertainty?
- A. 8.2 ± 0.3 cm
- B. 8.2 ± 0.2 cm
- C. 8.2 ± 0.15 cm
- D. 8.2 ± 0.1 cm
Q7. The mass of a body is measured with 2% uncertainty and its speed with 3% uncertainty. What is the percentage uncertainty in its kinetic energy ½mv²?
- A. 11%
- B. 8%
- C. 6%
- D. 5%
Q8. The product 12.25 × 2.1, written to the correct number of significant figures, is:
- A. 25.73
- B. 26
- C. 25.725
- D. 25.7
Q9. On a vernier calliper, 10 vernier divisions coincide with 9 main-scale divisions of 1 mm each. What is its least count?
- A. 0.1 mm
- B. 1 mm
- C. 0.9 mm
- D. 0.01 mm
Q10. A screw gauge has a negative zero error of 0.03 mm. It gives an observed reading of 4.52 mm for the diameter of a wire. What is the corrected diameter?
- A. 4.49 mm
- B. 4.55 mm
- C. 4.58 mm
- D. 4.52 mm
Q11. If A = 3i + 2j and B = i − 2j, what is the magnitude of A − B?
- A. 4
- B. 2√2
- C. 2√5
- D. 2√10
Q12. What angle does the vector A = i + √3 j make with the positive x-axis?
- A. 45°
- B. 30°
- C. 60°
- D. 120°
Q13. Using the right-hand rule for unit vectors, j × i equals:
- A. i
- B. 0
- C. −k
- D. k
Q14. What is (i + j) × (i − j)?
- A. 2k
- B. −2k
- C. 0
- D. k
Q15. For what value of m are the vectors 2i + 3j and 4i + mj parallel?
- A. −6
- B. 8/3
- C. 3
- D. 6
Q16. What is the cosine of the angle that A = 2i + 3j + 6k makes with the z-axis?
- A. 2/7
- B. 3/7
- C. 6/7
- D. 6/11
Q17. Two forces, each of magnitude F, act at a point with an angle of 120° between them. What is the magnitude of their resultant?
- A. F/2
- B. F
- C. √3 F
- D. 2F
Q18. Two forces of equal magnitude F have a resultant of magnitude √3 F. What is the angle between them?
- A. 30°
- B. 90°
- C. 60°
- D. 120°
Q19. A 50 N weight hangs from two strings attached to a ceiling. One string makes 30° and the other 60° with the horizontal. What is the tension in the string inclined at 60°?
- A. 50 N
- B. 50√3 N
- C. 25 N
- D. 25√3 N
Q20. A force F = (2i − j) N acts at a point with position vector r = (i + j) m. What is the magnitude of the torque about the origin?
- A. 2 N m
- B. √5 N m
- C. 1 N m
- D. 3 N m
Q21. A uniform horizontal beam 4 m long and weighing 200 N is hinged to a wall at one end and held up by a vertical rope at the other end. A 100 N load hangs 3 m from the hinge. What is the tension in the rope?
- A. 125 N
- B. 300 N
- C. 175 N
- D. 150 N
Q22. Masses of 2 kg and 3 kg are fixed at x = 0 and x = 5 m on a light rod. Where is the centre of gravity of the system?
- A. x = 3.5 m
- B. x = 2 m
- C. x = 3 m
- D. x = 2.5 m
Q23. A body is in neutral equilibrium if, when it is slightly displaced, its centre of gravity:
- A. rises
- B. moves outside its base
- C. stays at the same height
- D. falls
Q24. What is the minimum number of coplanar forces of unequal magnitudes whose vector sum can be zero?
- A. 5
- B. 4
- C. 2
- D. 3
Q25. For two vectors with |A| = 4 and |B| = 3, the scalar product is A·B = 6. What is |A × B|?
- A. 3√3
- B. 6√3
- C. 6
- D. 12
Q26. Two vectors A and B of equal magnitude are such that |A + B| = |A| = |B|. What is the angle between A and B?
- A. 90°
- B. 60°
- C. 120°
- D. 0°
Q27. A vector has an x-component of 6 units and a y-component of −8 units. Which description is correct?
- A. Magnitude 14 units, in the fourth quadrant
- B. Magnitude 10 units, in the second quadrant
- C. Magnitude 10 units, in the fourth quadrant
- D. Magnitude 2 units, in the fourth quadrant
Q28. Which statement about the torque of a couple is correct?
- A. It is zero because the two forces cancel
- B. It is the same about every axis perpendicular to the plane of the couple
- C. It produces linear acceleration of the body
- D. It depends on the position of the chosen axis
Q29. Which of these equations is dimensionally INCORRECT (v, u = speeds, a = acceleration, s = distance, t = time)?
- A. v = u + at²
- B. s = ut + ½at²
- C. v = u + at
- D. v² = u² + 2as
Q30. A nut needs a torque of 12 N m to loosen it. What force must be applied perpendicular to a spanner at 0.3 m from the nut?
- A. 36 N
- B. 40 N
- C. 4 N
- D. 3.6 N