ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Measurements, Vectors and Equilibrium (Set 7): 30 multiple-choice questions (40 minutes) with instant scoring and a full answer…
What this test covers
The first 5 questions of this test, with the correct answer and explanation.
Q1. The dimensions of the pressure gradient (change of pressure per unit length along the flow direction) are:
Answer: A. ML⁻²T⁻²
Explanation: Pressure = ML⁻¹T⁻²; dividing by length L gives ML⁻²T⁻².
Q2. The dimensions of specific heat capacity (heat per unit mass per kelvin) are:
Answer: D. L²T⁻²K⁻¹
Explanation: c = Q/(mΔT) = ML²T⁻²/(M·K) = L²T⁻²K⁻¹.
Q3. The small-amplitude oscillation period T of a liquid drop depends only on its density ρ, surface tension σ (force per unit length) and radius r, as T = k ρᵃσᵇrᶜ with k dimensionless. The value of c is:
Answer: A. 3/2
Explanation: [σ] = MT⁻². Powers of M: a + b = 0; of T: −2b = 1 so b = −1/2, a = 1/2; of L: −3a + c = 0 so c = 3/2.
Q4. The number of significant figures in the measurement 0.004050 m is:
Answer: C. 4
Explanation: Leading zeros are not significant; the digits 4, 0, 5, 0 (including the trailing zero after the decimal point) are significant: 4.
Q5. Three lengths 12.11 cm, 18.0 cm and 1.013 cm are added. Following the rule for addition (result limited by the least number of decimal places), the sum is:
Answer: D. 31.1 cm
Explanation: Sum = 31.123; 18.0 has one decimal place, so the result is 31.1 cm.
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Q6. The side of a cube is measured as (2.0 ± 0.1) cm. Using the rule that percentage uncertainties add for a product, its volume is:
Q7. In a pendulum experiment g = 4π²L/T². L is measured with 1% uncertainty and T with 2% uncertainty. The maximum percentage uncertainty in g is:
Q8. Two rod lengths are measured as (25.0 ± 0.2) mm and (12.0 ± 0.3) mm. Taking maximum uncertainties, which add for sums and differences, the difference of the lengths is:
Q9. A vernier caliper has a main scale graduated in millimetres and 20 vernier divisions equal to 19 main-scale divisions. The zero of the vernier lies just beyond the 14 mm mark and the 7th vernier division coincides with a main-scale division. The reading is:
Q10. A screw gauge has pitch 0.5 mm and 50 circular-scale divisions. With the jaws closed it reads −0.03 mm. A wire gives a main-scale reading of 3.0 mm and circular-scale reading of 27 divisions. Taking true reading = observed reading − zero error, the diameter is:
Q11. Two tugs pull on a barge with forces of 8 kN and 5 kN; the angle between their ropes is 120°. The magnitude of the net pull is:
Q12. Two vectors of magnitudes 7 and 10 units are added in all possible orientations. Which of the following cannot be the magnitude of their resultant?
Q13. The scalar component (projection) of the vector A = 4i + j + 3k along the vector B = i + 2j + 2k is:
Q14. For A = 2i + 3j and B = 4i − j, the k-component of the vector product A × B is:
Q15. A force F = (2i + 3j + k) N displaces a particle by d = (4i − j + 2k) m. The work done is:
Q16. A force F = (3i + 4j) N acts at the point whose position vector from the origin is r = (2i + j) m. The torque about the origin (taking out-of-page, +k, as positive) is:
Q17. A vector of magnitude 50 units makes an angle of 37° with the y-axis. Taking sin 37° = 0.6, its x-component is:
Q18. A 60 N weight is hung from the midpoint of a light string whose ends are fixed at the same level; each half of the string makes 30° with the horizontal. The tension in the string is:
Q19. A uniform ladder of length 5 m and weight 100 N rests with its upper end against a smooth vertical wall and its foot on rough ground 3 m from the wall. The horizontal reaction of the wall is:
Q20. A uniform beam 6 m long weighing 60 N rests on supports at its two ends. A 90 N load is placed 2 m from the left end. The reaction at the right support is:
Q21. Two equal and opposite parallel forces of 8 N act at the ends of a rod 0.5 m long, the rod being inclined at 30° to the lines of action of the forces. The moment of the couple is:
Q22. A uniform solid cone lying on a horizontal table with its curved surface touching the table is in:
Q23. Masses of 1 kg, 2 kg and 3 kg are placed at x = 0, 3 m and 6 m on a light rod. The centre of gravity is at x =
Q24. Three forces keep a particle in equilibrium: 4 N towards the east, 3 N towards the north and a third force F₃. Taking tan⁻¹(3/4) = 37°, F₃ is:
Q25. A uniform metre stick balances horizontally on a knife edge placed at the 40 cm mark when a 100 g mass is hung at the 10 cm mark. The mass of the stick is:
Q26. A processor clock runs at 5 GHz. Its period is:
Q27. A lab measures a rod whose true length is 9.50 cm and gets 10.02, 10.01, 10.03 and 10.02 cm. The readings are:
Q28. The cosine of the angle between the vectors P = 2i − j + 2k and Q = i + 2j − 2k is:
Q29. Two vectors, each of magnitude 6 units, are inclined at 60° to each other. The magnitude of their difference A − B is:
Q30. The unit vector along 3i − 4j + 12k has a j-component equal to: