ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Measurements, Vectors and Equilibrium (Set 5): 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. Planck's constant h has dimensions of energy × time. The quantity h/(m c), where m is a mass and c the speed of light, has the dimensions of:
Answer: A. length
Explanation: [h] = ML²T⁻¹, so h/(mc) = ML²T⁻¹/(M·LT⁻¹) = L. It is a length (the Compton wavelength h/mc).
Q2. The period of oscillation of a liquid drop is assumed to depend on its density ρ, radius r and surface tension σ as T = k ρᵃ rᵇ σᶜ. Using dimensions, the value of b is:
Answer: B. 3/2
Explanation: [σ] = MT⁻². M: a + c = 0. T: −2c = 1 so c = −1/2, a = 1/2. L: −3a + b = 0 so b = 3/2.
Q3. A body moves under a resisting force F = a v + b v², where v is the speed and a and b are constants. The ratio a/b has the dimensions of:
Answer: A. velocity
Explanation: [a] = F/v = MT⁻¹; [b] = F/v² = ML⁻¹. a/b = (MT⁻¹)/(ML⁻¹) = LT⁻¹, which is a velocity.
Q4. The mass of a solid cube is measured as 40.0 g with an uncertainty of 0.4 g, and its edge as 2.00 cm with an uncertainty of 0.02 cm. The percentage uncertainty in the density is:
Answer: C. 4 %
Explanation: ρ = m/a³. Percentage uncertainty = 0.4/40 ×100 + 3×(0.02/2)×100 = 1 % + 3 % = 4 %.
Q5. A potential difference is measured as V = 100 ± 5 V and the current as I = 10 ± 0.2 A. Using the rule that maximum fractional uncertainties add, the resistance R = V/I is quoted as:
Answer: D. 10.0 ± 0.7 Ω
Explanation: Fractional uncertainties add: 5/100 + 0.2/10 = 0.05 + 0.02 = 0.07. R = 10 Ω, so ΔR = 0.07×10 = 0.7 Ω.
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Q6. In a pendulum experiment, L = 1.000 m is measured with an uncertainty of 1 mm, and the time for 20 oscillations is 40.0 s with an uncertainty of 0.2 s. Using g = 4π²L/T², the percentage uncertainty in g is:
Q7. Multiplying 6.022 by 0.0030 on a calculator gives 0.018066. Keeping the correct number of significant figures, the result is:
Q8. A screw gauge has pitch 0.5 mm and 50 divisions on the circular scale. Its zero reading is +4 divisions. When a wire is gripped, the main scale shows 2.0 mm and the circular scale reading is 31 divisions. The diameter of the wire is:
Q9. One atmosphere is 1.01 × 10⁵ N m⁻². Expressed in N cm⁻², it is approximately:
Q10. A runner covers a distance of 100 m, measured to ±1 m, in a time of 12.5 s, measured to ±0.25 s. The speed is best reported as:
Q11. A vector A = i + j and a vector B = j + k are drawn from the same point. The angle between them is:
Q12. The component of the vector A = 2i + 3j + 6k along the direction of B = 3i + 4k is:
Q13. A triangle has one vertex at the origin and the other two at the points (1, 2, 2) and (2, 1, −2) in metres. Its area is:
Q14. The vectors A = 3i + p j − 6k and B = −i + 2j + q k are parallel. The product p q is:
Q15. Two forces of 7 N and 8 N act at a point with 60° between their directions. The magnitude of their resultant is:
Q16. Two forces of 6 N and 10 N act at a point. Which of the following cannot be the magnitude of their resultant?
Q17. A drone flies 6 m east, then 8 m north, and then rises vertically 24 m. The magnitude of its displacement from the start is:
Q18. A vector has components Vₓ = −3 units and V_y = +4 units. The angle it makes with the positive x-axis, measured anticlockwise, is closest to:
Q19. A vector makes angles of 60° with the x-axis and 60° with the y-axis. The angle it makes with the z-axis (taking it as acute) is:
Q20. A particle is at position r = 3j m and a force F = 4i N acts on it. The torque about the origin, τ = r × F, is:
Q21. For two vectors A and B it is found that A·B = |A × B|. The angle between them is:
Q22. A force of 20 N is applied at the free end of a 2 m rod pivoted at its other end. The force makes 30° with the rod. The magnitude of the torque about the pivot is:
Q23. A force F = 2i − 3j + 4k N displaces a body by d = 5i + 2j + k m. The work done is:
Q24. Take g = 10 m s⁻² and sin37° = 0.6, cos37° = 0.8. A 3 kg block is held at rest on a smooth plane inclined at 37° by a horizontal force F pushing into the slope. The magnitude of F is:
Q25. A uniform plank 4 m long weighing 80 N rests on supports at its two ends. A 120 N load is placed 1 m from the left end. The reaction at the right support is:
Q26. A uniform ladder of weight 400 N leans against a smooth vertical wall, making an angle with the ground whose tangent is 4/3. The friction force at the ground needed for equilibrium is:
Q27. A couple acts on a rigid body. Which statement about its torque is correct?
Q28. A uniform rod 1.2 m long weighs 30 N and carries a 20 N weight attached at one end. The distance of the balance point from the loaded end is:
Q29. A uniform solid block is 20 cm wide at its base and 40 cm tall, and rests on an inclined plane that is gradually tilted. Assuming it does not slide, it begins to topple when tan θ equals:
Q30. A uniform horizontal rod of weight 100 N is hinged to a wall at one end. Its free end is supported by a light cable attached to that free end and making 30° with the rod. The tension in the cable is: