Physics Mock Test 6 Practice

1. The dimensional formula of coefficient of viscosity η is:

• A. [ML⁻¹T⁻¹] (Correct)
• B. [MLT⁻¹]
• C. [ML⁻²T⁻¹]
• D. [ML²T⁻²]

Explanation: From Newton's law of viscosity: F = ηA(dv/dx). η = F/(A × dv/dx) = [MLT⁻²]/([L²][T⁻¹]) = [ML⁻¹T⁻¹] .

2. If A = 2î + 3ĵ − k̂ and B = î − 2ĵ + 3k̂, then A·B is:

• A. −7 (Correct)
• B. 7
• C. −4
• D. 4

Explanation: A·B = (2)(1) + (3)(−2) + (−1)(3) = 2 − 6 − 3 = −7 .

3. A particle starts with velocity 10 m/s and has constant deceleration 2 m/s². The total distance before it stops and returns to start is:

• A. 25 m
• B. 50 m (Correct)
• C. 0 m
• D. 100 m

Explanation: Distance to stop: s₁ = v²/2a = 100/4 = 25 m. On return it covers another 25 m. Total = 50 m .

4. A ball is thrown with velocity 40 m/s at 30° to horizontal. The horizontal range (g = 10 m/s²) is:

• A. 40√3 m
• B. 80 m
• C. 160√3 m
• D. 80√3 m (Correct)

Explanation: R = u²sin2θ/g = 1600×sin60°/10 = 1600×(√3/2)/10 = 80√3 m .

5. Three blocks (2 kg, 3 kg, 5 kg) are connected in series on frictionless surface. Force F = 30 N on the 5 kg block. Tension between 3 kg and 2 kg blocks is:

• A. 3 N
• B. 6 N (Correct)
• C. 9 N
• D. 15 N

Explanation: a = F/(2+3+5) = 30/10 = 3 m/s². Tension on 2 kg block: T = 2×3 = 6 N .

6. Power is defined as:

• A. Work × Time
• B. Work / Time (Correct)
• C. Force × Velocity²
• D. Energy / Mass

Explanation: P = W/t = Work / Time .

7. Torque 10 N·m acts on flywheel (I = 2 kg·m²). Angular acceleration:

• A. 20 rad/s²
• B. 5 rad/s² (Correct)
• C. 0.2 rad/s²
• D. 2 rad/s²

Explanation: α = τ/I = 10/2 = 5 rad/s² .

8. Gravitational potential inside uniform solid sphere at distance r < R from centre:

• A. −GM/r
• B. −GM/R
• C. −GM(3R²−r²)/2R³ (Correct)
• D. Zero

Explanation: Inside solid sphere: V = −GM(3R²−r²)/(2R³) = −GM(3R²−r²)/2R³ .

9. Thermal stress in a rod (Y, α, ΔT) when ends are fixed:

• A. YαΔT (Correct)
• B. αΔT/Y
• C. Y/αΔT
• D. YΔT/α

Explanation: Thermal strain = αΔT. Thermal stress = Y × αΔT = YαΔT .

10. Hole in tank at middle (h = H/2). Speed of efflux vs hole at bottom (h = H):

• A. Same
• B. 1/√2 times (Correct)
• C. √2 times
• D. Half

Explanation: v ∝ √h. v_mid/v_bottom = √(H/2)/√H = 1/√2 .

11. In a NEET physics drill, a particle starts with speed 7 m/s and acceleration 2 m/s^2 for 5 s. Final speed is:

• A. 15 m/s
• B. 19 m/s
• C. 35 m/s
• D. 17 m/s (Correct)

Explanation: Use v = u + at = 7 + 2 x 5 = 17 m/s.

12. Which of the following sets of quantities are all dimensionless?

• A. Strain, angle, refractive index (Correct)
• B. Frequency, velocity, acceleration
• C. Strain, temperature, pressure
• D. Angle, momentum, energy

Explanation: Strain = ΔL/L (dimensionless), angle = arc/radius (dimensionless), refractive index = c/v (dimensionless). All three are dimensionless quantities.

13. If v = u + at (where u, a are constants), then the displacement from t = 0 to t = T is:

• A. uT + aT²
• B. uT + (1/2)aT² (Correct)
• C. uT − (1/2)aT²
• D. (1/2)aT²

Explanation: s = ∫₀ᵀ (u + at) dt = [ut + at²/2]₀ᵀ = uT + (1/2)aT² . This is the standard kinematic equation.

14. A rocket is fired vertically with net upward acceleration a for time T. After T, it goes into free fall. The maximum height above ground is:

• A. ½aT²
• B. aT²
• C. ½aT² + a²T²/2g (Correct)
• D. aT²/2g

Explanation: Height at burnout: h₁ = ½aT². Velocity at burnout: v = aT. Extra height: h₂ = v²/2g = a²T²/2g. Total max height = ½aT² + a²T²/2g .

15. The acceleration in uniform circular motion is called:

• A. Tangential acceleration
• B. Angular acceleration
• C. Centripetal acceleration (Correct)
• D. Linear acceleration

Explanation: In uniform circular motion, speed is constant. The acceleration toward center is centripetal acceleration .

16. A car (1000 kg) moving at 20 m/s is brought to rest in 4 s. The braking force is:

• A. 5000 N (Correct)
• B. 80000 N
• C. 200 N
• D. 50 N

Explanation: a = 20/4 = 5 m/s². F = ma = 1000×5 = 5000 N .

17. SI unit of power is:

• A. Joule
• B. Newton
• C. Watt (Correct)
• D. Pascal

Explanation: Power SI unit is Watt (W) = J/s.

18. A solid cylinder rolls without slipping on a horizontal surface. Its total KE:

• A. ½Mv²
• B. ¾Mv² (Correct)
• C. Mv²
• D. ½Mv²/2

Explanation: KE_total = ½Mv² + ½×½MR²×(v/R)² = ½Mv² + ¼Mv² = ¾Mv² .

19. Angular momentum of satellite in circular orbit:

• A. Constant (Correct)
• B. Increases
• C. Decreases
• D. Zero

Explanation: In circular orbit, no net torque (gravity is central). Angular momentum = constant .

20. Steel rod (Y=2×10¹¹, α=10⁻⁵ /°C) heats by 10°C (ends fixed). Thermal stress:

• A. 2×10⁷ Pa (Correct)
• B. 2×10⁸ Pa
• C. 2×10⁶ Pa
• D. 2×10⁹ Pa

Explanation: σ = YαΔT = 2×10¹¹×10⁻⁵×10 = 2×10⁷ Pa .

21. Venturimeter: inlet area A₁, throat area A₂, pressure difference ΔP. Volume flow Q:

• A. A₁A₂√(2ΔP/ρ(A₁²−A₂²)) (Correct)
• B. A₁A₂√(2ΔP/ρ)/A₁
• C. ΔP×A₂
• D. A₂√(2ΔP/ρ)

Explanation: Standard venturimeter formula: Q = A₁A₂√(2ΔP/ρ(A₁²−A₂²)) .

22. A block of mass 4 kg accelerates at 3 m/s^2. Net force on it is:

• A. 9 N
• B. 18 N
• C. 12 N (Correct)
• D. 15 N

Explanation: By Newton's second law, F = ma = 4 x 3 = 12 N.

23. The mean absolute error in five measurements of time: 2.63, 2.56, 2.42, 2.71, 2.80 seconds is approximately:

• A. 0.10 s
• B. 0.11 s (Correct)
• C. 0.12 s
• D. 0.13 s

Explanation: Mean = 13.12/5 = 2.624 s. Deviations: |0.006|, |0.064|, |0.204|, |0.086|, |0.176|. Mean absolute error = 0.536/5 ≈ 0.11 s .

24. A × B = −(B × A) illustrates which property of cross product?

• A. Distributive property
• B. Anti-commutative property (Correct)
• C. Associative property
• D. Commutative property

Explanation: The cross product is anti-commutative : A × B = −(B × A). Reversing the order of vectors reverses the direction of the resultant.

25. A ball is thrown vertically upward with velocity 30 m/s from the top of a 45 m tower (g = 10 m/s²). The velocity when it hits the ground is:

• A. 30 m/s
• B. 40 m/s (Correct)
• C. 50 m/s
• D. 60 m/s

Explanation: Taking downward as positive: at ground, v² = u² + 2g(H+h) where H = 45 m, and the ball first goes up then comes down. Using energy: v² = (30)² + 2(10)(45) = 900 + 900 = 1800... v = √1800 ≈ 42. Or: total downward distance from highest point = 45 + 30²/(2×10) = 45+45 = 90 m. v² = 2×10×90 = 1800, v ≈ 42.4. Closest: 40 m/s .

26. A ball is kicked at 60° to the ground with speed 20 m/s (g = 10 m/s²). The maximum height is:

• A. 10 m
• B. 15 m (Correct)
• C. 20 m
• D. 5 m

Explanation: H = u²sin²θ/2g = 400×(3/4)/20 = 15 m .

27. Newton's third law action-reaction pair acts on:

• A. The same body
• B. Different bodies (Correct)
• C. Same body in same direction
• D. Different bodies in same direction

Explanation: Action-reaction forces always act on different bodies . They are equal in magnitude and opposite in direction.

28. Motor lifts 1000 kg water to 20 m in 10 s (g = 10 m/s²). Power of motor:

• A. 2 kW
• B. 20 kW (Correct)
• C. 200 kW
• D. 200 W

Explanation: P = mgh/t = 1000×10×20/10 = 20,000 W = 20 kW .

29. A solid sphere rolls down incline from height h (no slipping). Speed at bottom:

• A. √(2gh)
• B. √(10gh/7) (Correct)
• C. √(4gh/3)
• D. √(gh)

Explanation: mgh = ½mv²(1+I/mR²) = ½mv²×7/5. v² = 10gh/7. v = √(10gh/7) .

30. Geostationary satellite has period:

• A. 12 hours
• B. 24 hours (Correct)
• C. 48 hours
• D. 1 hour

Explanation: Geostationary = stationary relative to Earth. Period = 24 hours (same as Earth's rotation).

31. Brittle material on stress-strain curve:

• A. Large plastic region before fracture
• B. Fractures abruptly at or just beyond elastic limit (Correct)
• C. Identical to ductile
• D. Never fractures

Explanation: Brittle materials (glass, cast iron): fracture abruptly with little or no plastic deformation.

32. Two buildings close together experience strong wind between them. The corridor is dangerous because:

• A. High temperature
• B. High pressure between buildings
• C. Low pressure between buildings (Bernoulli) can suck walls (Correct)
• D. High velocity = high pressure

Explanation: Faster wind between buildings → lower pressure (Bernoulli) → can create suction forces .

33. A spring of constant 140 N/m is compressed by 0.1 m. Energy stored is:

• A. 14 J
• B. 0.7 J (Correct)
• C. 1.4 J
• D. 0.35 J

Explanation: Spring energy = (1/2)kx^2 = 0.5 x 140 x 0.01 = 0.7 J.

34. The dimensions of (μ₀ε₀)⁻¹/² are the same as:

• A. Velocity (Correct)
• B. Acceleration
• C. Force
• D. Energy

Explanation: 1/√(μ₀ε₀) = c, the speed of light. So (μ₀ε₀)⁻¹/² has dimensions of velocity [LT⁻¹].

35. The velocity of a particle is v = A cos(ωt). The acceleration is:

• A. −Aω sin(ωt) (Correct)
• B. Aω sin(ωt)
• C. −Aω² cos(ωt)
• D. Aω² cos(ωt)

Explanation: a = dv/dt = d[A cos(ωt)]/dt = −Aω sin(ωt) .

36. The displacement of a particle varies with time as x = 4t − t² (in SI units). When does the particle return to the origin?

• A. t = 2 s
• B. t = 4 s (Correct)
• C. t = 8 s
• D. t = 1 s

Explanation: x = 0: 4t − t² = 0 → t(4−t) = 0 → t = 0 or t = 4 s . At t = 0 (start) and t = 4 s (returns to origin).

37. A stone on a 1 m string whirled in vertical circle. Minimum speed at top to maintain circular motion (g = 10 m/s²) is:

• A. √10 m/s (Correct)
• B. √5 m/s
• C. 10 m/s
• D. 5 m/s

Explanation: v_min = √(gr) = √(10×1) = √10 m/s .

38. A block (5 kg) pushed against rough wall (μ = 0.5) by horizontal force 100 N. Friction force (g = 10 m/s²):

• A. 50 N (Correct)
• B. 25 N
• C. 100 N
• D. 250 N

Explanation: Weight = 5×10 = 50 N. Max friction = μN = 0.5×100 = 50 N. Block stays. Friction = weight = 50 N .

39. Car (1000 kg) accelerates from 0 to 30 m/s in 10 s. Average power:

• A. 45,000 W (Correct)
• B. 90,000 W
• C. 30,000 W
• D. 15,000 W

Explanation: W = ½×1000×900 = 450,000 J. P = 450,000/10 = 45,000 W .

40. A ladder (mass M, length L) leans against smooth wall at angle θ. Friction at floor for equilibrium:

• A. Mg tanθ/2
• B. Mg/2tanθ
• C. Mg cosθ/2sinθ (Correct)
• D. Mg/2

Explanation: Taking torques about base: N_wall×L sinθ = Mg×(L/2)cosθ. f = N_wall = Mg cosθ/(2sinθ) = Mg cosθ/2sinθ .

41. Equipotential surfaces due to a point mass are:

• A. Planes
• B. Cylinders
• C. Concentric spheres (Correct)
• D. Ellipsoids

Explanation: V = −GM/r = constant on surfaces of equal r. These are concentric spheres .

42. If stress doubles (same material), elastic PE per unit volume:

• A. Doubles
• B. Halves
• C. Quadruples (Correct)
• D. Stays same

Explanation: u = σ²/2Y. σ→2σ: u → 4u = quadruples .

43. Ideal fluid is incompressible and:

• A. Viscous
• B. Non-viscous (inviscid) (Correct)
• C. Static
• D. Turbulent

Explanation: Ideal fluid is incompressible and non-viscous . Bernoulli's equation applies to ideal fluids.

44. A body moves in a circle of radius 4 m with speed 4 m/s. Centripetal acceleration is:

• A. 4 m/s^2 (Correct)
• B. 6 m/s^2
• C. 2 m/s^2
• D. 16 m/s^2

Explanation: Centripetal acceleration = v^2/r = 16/4 = 4 m/s^2.

45. If x = a + b, the maximum absolute error in x when errors in a and b are Δa and Δb respectively is:

• A. Δa − Δb
• B. Δa × Δb
• C. Δa + Δb (Correct)
• D. |Δa − Δb|

Explanation: For addition or subtraction, absolute errors add up: Δx = Δa + Δb (maximum error). This ensures we account for worst-case combination of errors.

46. The function f(x) = x² − 4x + 5 has a minimum value of:

• A. 1 (Correct)
• B. 5
• C. 4
• D. 0

Explanation: f'(x) = 2x − 4 = 0 → x = 2. f(2) = 4 − 8 + 5 = 1 . Since f''(x) = 2 > 0, this is a minimum.

47. A cyclist covers 200 m in 20 s. His average speed is:

• A. 10 m/s (Correct)
• B. 20 m/s
• C. 4000 m/s
• D. 0.1 m/s

Explanation: Average speed = 200/20 = 10 m/s .

48. The SI unit of angular velocity is:

• A. degree/s
• B. rad/s (Correct)
• C. rpm
• D. rev/s

Explanation: The SI unit of angular velocity is radian per second (rad/s) .

49. A body of mass m is pulled by force F at angle θ above horizontal on rough surface. Normal force is:

• A. mg
• B. mg − Fsinθ (Correct)
• C. mg + Fsinθ
• D. mg − Fcosθ

Explanation: Vertical equilibrium: N + Fsinθ = mg → N = mg − Fsinθ .

50. 100 N force acts on body moving at 5 m/s. Instantaneous power:

• A. 20 W
• B. 500 W (Correct)
• C. 105 W
• D. 95 W

Explanation: P = Fv = 100 × 5 = 500 W .

51. Angular impulse equals:

• A. τ/t
• B. τ×t (Correct)
• C. τ×α
• D. Iα

Explanation: Angular impulse = τ×Δt = ΔL. Analogous to linear impulse F×t = Δp. = τ×t .

52. According to Kepler's 2nd law, planet moves fastest when:

• A. Farthest from Sun (aphelion)
• B. Closest to Sun (perihelion) (Correct)
• C. At average distance
• D. Speed is always same

Explanation: At perihelion (closest point), by conservation of angular momentum, planet moves fastest.

53. For an auxetic material, Poisson's ratio is:

• A. 0 to 0.5
• B. Exactly 0.5
• C. Negative (Correct)
• D. >1

Explanation: Auxetic materials expand laterally when stretched — they have negative Poisson's ratio .

54. Spray pumps and perfume atomizers work on:

• A. Pascal's law
• B. Archimedes' principle
• C. Bernoulli's effect (fast air creates low pressure) (Correct)
• D. Capillarity

Explanation: Spray pumps: fast air over nozzle → low pressure → liquid sucked up. Bernoulli's effect .

55. Two perpendicular vectors have magnitudes 4 and 4. Their resultant magnitude is approximately:

• A. 8
• B. 0
• C. 16.0
• D. 5.7 (Correct)

Explanation: For perpendicular vectors, R = sqrt(4^2 + 4^2) = 5.7.

56. The number of base quantities in the SI system is:

• A. 5
• B. 6
• C. 7 (Correct)
• D. 8

Explanation: The SI system has 7 base quantities: length (m), mass (kg), time (s), electric current (A), thermodynamic temperature (K), amount of substance (mol), luminous intensity (cd).

57. The angle between vectors A = î + ĵ and B = î − ĵ is:

• A. 0°
• B. 45°
• C. 90° (Correct)
• D. 180°

Explanation: A·B = (1)(1) + (1)(−1) = 0. Since dot product is zero, the vectors are perpendicular: θ = 90° .

58. A body accelerates from rest to 10 m/s in 5 s, then decelerates to rest in 10 s. The total distance is:

• A. 75 m (Correct)
• B. 125 m
• C. 100 m
• D. 25 m

Explanation: Phase 1: s₁ = ½(0+10)(5) = 25 m. Phase 2: s₂ = ½(10+0)(10) = 50 m. Total = 75 m .

59. A particle travels in a semicircle of diameter 10 m. Its displacement is:

• A. 5π m
• B. 10 m (Correct)
• C. 20 m
• D. 5 m

Explanation: Displacement = diameter = 10 m . Distance = πr = 5π m.

60. Mass 2 kg acted on by force 6î + 8ĵ N for 3 s (starting from rest). Velocity acquired:

• A. 9î + 12ĵ m/s (Correct)
• B. 3î + 4ĵ m/s
• C. 18î + 24ĵ m/s
• D. 6î + 8ĵ m/s

Explanation: a = F/m = (6î+8ĵ)/2 = 3î+4ĵ m/s². v = at = (3î+4ĵ)×3 = 9î+12ĵ m/s .