ECAT — Engineering College Admission Test (UET)

ECAT Physics — Measurements, Vectors and Equilibrium (Set 1)

Take the ECAT Physics — Measurements, Vectors and Equilibrium (Set 1): 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. What are the dimensions of Planck's constant h (from E = hf)?
- A. [ML²T⁻³]
- B. [ML²T⁻²]
- C. [MLT⁻¹]
- D. [ML²T⁻¹] ✓
Answer: D. [ML²T⁻¹]
Explanation: h = E/f, so [ML²T⁻²]/[T⁻¹] = [ML²T⁻¹], the same as angular momentum.
Q2. The radius of a sphere is measured with an uncertainty of 2%. What is the percentage uncertainty in its volume?
- A. 2%
- B. 6% ✓
- C. 8%
- D. 4%
Answer: B. 6%
Explanation: V ∝ r³, so the percentage uncertainty is 3 × 2% = 6%.
Q3. How many significant figures are there in 0.004050?
- A. 6
- B. 4 ✓
- C. 3
- D. 7
Answer: B. 4
Explanation: Leading zeros are not significant; 4, 0, 5 and the trailing 0 after the decimal point are significant, giving 4.
Q4. In a simple pendulum experiment g = 4π²l/T². If l is measured with 1% uncertainty and T with 0.5% uncertainty, what is the percentage uncertainty in g?
- A. 1.5%
- B. 2% ✓
- C. 0.5%
- D. 3%
Answer: B. 2%
Explanation: %g = %l + 2(%T) = 1% + 2(0.5%) = 2%.
Q5. Which pair of physical quantities has the same dimensions?
- A. Power and pressure
- B. Momentum and energy
- C. Work and torque ✓
- D. Force and impulse
Answer: C. Work and torque
Explanation: Both work (F·d) and torque (r × F) have dimensions [ML²T⁻²], though torque is not measured in joules.

The other 25 questions

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Q6. What are the dimensions of the gravitational constant G (F = Gm₁m₂/r²)?
- A. [ML³T⁻²]
- B. [M⁻¹L³T⁻²]
- C. [M⁻²L³T⁻²]
- D. [M⁻¹L²T⁻²]
Q7. A force varies with time as F = at + bt². What are the dimensions of b?
- A. [MLT⁻³]
- B. [MLT⁻¹]
- C. [MLT⁻²]
- D. [MLT⁻⁴]
Q8. Find the magnitude of the resultant of A = i + 2j + 3k and B = i − 5j + 3k.
- A. √13
- B. 11
- C. 5
- D. 7
Q9. Find the scalar product of A = 2i + 3j − k and B = i − 2j + 4k.
- A. 0
- B. -8
- C. −4
- D. 8
Q10. What is the angle between the vectors i + j and j + k?
- A. 60°
- B. 90°
- C. 45°
- D. 30°
Q11. What is the area of the parallelogram whose adjacent sides are A = 2i and B = 3j + 4k (in m)?
- A. 14 m²
- B. 10 m²
- C. 24 m²
- D. 5 m²
Q12. For what value of p are A = 2i + pj + k and B = i − 2j + 4k perpendicular?
- A. -3
- B. 3
- C. 2
- D. 6
Q13. Two forces of 5 N and 3 N act at a point with an angle of 60° between them. What is the magnitude of their resultant?
- A. 6 N
- B. √19 N
- C. 7 N
- D. 8 N
Q14. The maximum and minimum resultants of two forces are 17 N and 7 N. What is their resultant when they act at right angles?
- A. 10 N
- B. 13 N
- C. 12 N
- D. 17 N
Q15. What is the projection of A = 4i + 3j on the direction of B = 3i + 4j?
- A. 4.8
- B. 24
- C. 0.96
- D. 5
Q16. A rope pulls a sledge with a tension of 20 N directed 30° above the horizontal. What vertical (upward) pull does the rope exert on the sledge?
- A. 10 N
- B. 11.5 N
- C. 20 N
- D. 17.3 N
Q17. Which statement about the vector product is correct?
- A. A × A = A²
- B. A × B = −(B × A)
- C. A × B = B × A
- D. |A × B| = AB cos θ
Q18. A force F = (2i + 3j) N acts at a point whose position vector from the axis is r = 4i m. What is the torque τ = r × F?
- A. 12i N m
- B. 12k N m
- C. 8k N m
- D. −12k N m
Q19. A 50 N force is applied at the edge of a door, 0.4 m from the hinge, at 30° to the plane of the door. What torque does it produce about the hinge?
- A. 10 N m
- B. 5 N m
- C. 17.3 N m
- D. 20 N m
Q20. If the net force on a rigid body is zero but the net torque is not zero, the body will:
- A. move with constant angular velocity
- B. have angular acceleration but no linear acceleration
- C. be in complete equilibrium
- D. have linear acceleration but no rotation
Q21. A uniform 2 m rod of weight 40 N rests on supports at its two ends. A 60 N load is hung 0.5 m from the left end. What is the reaction at the left support?
- A. 45 N
- B. 65 N
- C. 35 N
- D. 50 N
Q22. A 100 N weight hangs from two strings, each making 60° with the vertical. What is the tension in each string?
- A. 50 N
- B. 200 N
- C. 57.7 N
- D. 100 N
Q23. Three forces of 3 N, 4 N and 5 N acting at a point keep it in equilibrium. What is the angle between the 3 N and 4 N forces?
- A. 60°
- B. 90°
- C. 120°
- D. 180°
Q24. Two equal and opposite parallel forces of 10 N act on a body, their lines of action being 0.3 m apart. What is the moment of the couple?
- A. 6 N m
- B. 1.5 N m
- C. 3 N m
- D. 30 N m
Q25. What is the unit vector in the direction of 3i − 4j?
- A. (3i + 4j)/5
- B. (3i − 4j)/25
- C. (3i − 4j)/7
- D. (3i − 4j)/5
Q26. A screw gauge has a pitch of 0.5 mm and 50 divisions on its circular scale. What is its least count?
- A. 0.1 mm
- B. 0.01 mm
- C. 0.001 mm
- D. 0.05 mm
Q27. Which statement about precision and accuracy is correct? (Use the definitions in the Punjab FSc Physics textbook.)
- A. Accuracy depends only on the least count of the instrument
- B. Precision depends on the instrument's least count; accuracy depends on the fractional uncertainty
- C. Precision and accuracy mean the same thing
- D. A precise measurement is always accurate
Q28. A uniform metre rule is balanced on a knife-edge at its 50 cm mark. A 30 g mass hangs at the 10 cm mark. Where must a 40 g mass be hung to restore balance?
- A. At the 80 cm mark
- B. At the 60 cm mark
- C. At the 70 cm mark
- D. At the 90 cm mark
Q29. Two non-zero vectors P and Q satisfy |P + Q|² = |P − Q|². Which conclusion is correct?
- A. P and Q are antiparallel
- B. P and Q are parallel
- C. P and Q must have equal magnitudes
- D. P and Q are perpendicular
Q30. If |A × B| = √3 (A·B), what is the angle between A and B?
- A. 60°
- B. 90°
- C. 45°
- D. 30°