ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Measurements, Vectors and Equilibrium (Set 4): 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. Which of the following has the same dimensions as the Compton wavelength h/(mc), where h is Planck's constant, m a mass and c the speed of light?
Answer: B. Length
Explanation: [h] = ML²T⁻¹, [mc] = MLT⁻¹, so h/(mc) = L. It is a length.
Q2. The period T of oscillation of a liquid drop depends on its density ρ, radius r and surface tension σ as T ∝ ρᵃrᵇσᶜ. What is the value of b? (σ has dimensions MT⁻².)
Answer: C. 3/2
Explanation: M: a + c = 0; L: −3a + b = 0; T: −2c = 1. So c = −1/2, a = 1/2, b = 3/2.
Q3. The mass of a cube is measured as (40 ± 0.4) g and its side as (2.0 ± 0.02) cm. The percentage uncertainty in the calculated density is
Answer: D. 4%
Explanation: ρ = m/a³: 0.4/40 = 1% for mass and 3 × (0.02/2.0) = 3% for the volume. Adding gives 4%.
Q4. A quantity is calculated as Q = a²b/√c. If a, b and c have percentage uncertainties of 2%, 3% and 4% respectively, the percentage uncertainty in Q is
Answer: A. 9%
Explanation: Percentage uncertainties add with multiplying powers: 2(2) + 3 + ½(4) = 4 + 3 + 2 = 9%.
Q5. Three lengths 12.0 cm, 0.456 cm and 3.2 cm are added. The result, quoted to the correct number of significant figures, is
Answer: B. 15.7 cm
Explanation: The sum is 15.656 cm. In addition the result keeps the least number of decimal places (one, from 12.0 and 3.2), so 15.7 cm.
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Q6. How many significant figures does the measurement 0.0305030 m have?
Q7. A vernier callipers has least count 0.01 cm. With the jaws closed its zero is 3 divisions to the left of the main-scale zero (negative zero error). It reads 3.47 cm on a rod. The correct length is
Q8. A screw gauge has pitch 0.5 mm and 50 divisions on the circular scale. Its zero error is +4 divisions. For a wire the reading is 3 mm on the linear scale and 27 divisions on the circular scale. The diameter of the wire is
Q9. If A = î + 2ĵ + 2k̂ and B = 2î + ĵ − 2k̂, the magnitude of A × B is
Q10. The vectors A = λî + 3ĵ − 2k̂ and B = 2î + λĵ + 5k̂ are perpendicular. The value of λ is
Q11. Two forces of 3 N and 6 N act at a point. The angle between them for which the resultant is perpendicular to the 3 N force is
Q12. The maximum and minimum magnitudes of the resultant of two vectors are 14 units and 2 units. The magnitude of the resultant when the vectors are at right angles is
Q13. A force of 20 N makes an angle of 30° with the y-axis. Its component along the x-axis is
Q14. A vector of magnitude 21 units is directed along 2î − 3ĵ + 6k̂. The vector is
Q15. A vector makes angles of 45° with the x-axis and 60° with the y-axis, and an acute angle γ with the z-axis. The value of γ is
Q16. A force of 40 N is applied to a spanner of length 0.5 m, the force making an angle of 150° with the spanner. The torque is
Q17. A force F = 2k̂ N acts at the point r = (3î + 4ĵ) m. The magnitude of the torque about the origin is
Q18. A uniform horizontal beam 6 m long weighs 200 N and rests on supports at its two ends. A 300 N load is placed 2 m from the left end. The reaction at the left support is
Q19. A uniform ladder of weight 400 N and length 5 m rests with its foot on rough ground 3 m from a smooth vertical wall. The friction force at the foot is
Q20. Two equal strings make an angle of 120° with each other and together support a hanging weight W. The tension in each string is
Q21. Forces of 10 N are applied to a body, equal and opposite, along lines 0.3 m apart. If they are replaced by forces of 25 N with the same turning effect, the separation of their lines must be
Q22. A solid cone lies on its curved surface on a horizontal table. It is rolled slightly and released. The cone is in
Q23. Which quantity has the same dimensions as torque?
Q24. Which of these equations is dimensionally inconsistent? (s = displacement, u, v = velocities, a = acceleration, t = time)
Q25. A pressure is given as 2.5 g cm⁻¹ s⁻². In SI units it is
Q26. Two lengths are measured as A = (10.5 ± 0.1) cm and B = (4.5 ± 0.1) cm. The percentage uncertainty in the difference A − B is
Q27. Five readings of a length are 2.63, 2.56, 2.42, 2.71 and 2.80 cm. Taking the mean absolute deviation as the uncertainty, the result is
Q28. Which set of three forces (in newtons) can be in equilibrium when applied at a point?
Q29. The component of A = 4î + 3ĵ + 2k̂ along B = 2î + ĵ + 2k̂ is
Q30. Two vectors A and B have equal magnitudes, and the magnitude of A + B is equal to the magnitude of A. The angle between A and B is