Questions & explanations
1. Which of the following statements correctly defines pressure in a fluid and states Pascal's law?
- Pressure is a scalar quantity, and Pascal's law states that the pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the container.
- Pressure is a vector quantity, and Pascal's law states that the pressure in a fluid varies linearly with depth.
- Pressure is a scalar quantity, and Pascal's law states that the pressure at a point in a fluid is the same in all directions only if the fluid is at rest.
- Pressure is a scalar quantity, and Pascal's law states that the pressure in a moving fluid decreases as its speed increases.
Answer: Pressure is a scalar quantity, and Pascal's law states that the pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the container.
Pressure is indeed a scalar quantity (force per unit area, with no direction inherent to the pressure itself). Pascal's law correctly describes that an external pressure applied to an enclosed incompressible fluid is transmitted equally throughout the fluid. Options mentioning variation with depth (B) refer to hydrostatic pressure, not Pascal's law; option C incorrectly limits the law to fluids at rest (Pascal's law applies even when the fluid is moving as long as it is enclosed); option D refers to Bernoulli's principle, not Pascal's law.
2. Which of the following is NOT an application of surface tension?
- A: Cleaning action of detergents
- B: Capillary rise of water in a thin tube
- C: Convection currents in a liquid
- D: Floating of a needle on water
Answer: C: Convection currents in a liquid
Convection currents arise from density differences caused by temperature gradients, not from surface tension. In contrast, detergents clean by reducing surface tension to improve wetting; capillary rise depends on surface tension and adhesion; and a needle floats on water due to the surface tension of the liquid. Hence, only option C is not an application of surface tension.
3. Which of the following correctly explains the dynamic lift on an aeroplane wing?
- The pressure above the wing is higher than below.
- The air speed above the wing is lower than below.
- The air speed above the wing is higher, causing lower pressure above.
- The lift is due to the buoyant force of air.
Answer: The air speed above the wing is higher, causing lower pressure above.
According to Bernoulli's principle, where velocity is higher, pressure is lower. The curved upper surface of the wing forces air to travel faster above than below, creating a pressure difference that results in an upward dynamic lift. The other options are incorrect as they reverse the relationship or misattribute the cause.
4. A wire of length 2 m and cross-sectional area 4 × 10⁻⁶ m² is subjected to a tensile load of 100 N. If the Young's modulus of the material is 2 × 10¹¹ N/m², the elongation of the wire is:
- 0.25 mm
- 0.50 mm
- 1.00 mm
- 2.00 mm
Answer: 0.25 mm
Using the formula for elongation ΔL = (F L) / (A Y). Substituting F = 100 N, L = 2 m, A = 4 × 10⁻⁶ m², Y = 2 × 10¹¹ N/m² gives ΔL = (100 × 2) / (4 × 10⁻⁶ × 2 × 10¹¹) = 200 / (8 × 10⁵) = 2.5 × 10⁻⁴ m = 0.25 mm. The other options correspond to common miscalculations such as using the wrong area or incorrect unit conversion.
5. Which of the following correctly distinguishes laminar flow from turbulent flow?
- In laminar flow, velocity at any point remains constant; in turbulent flow, it varies randomly.
- Laminar flow has no viscosity; turbulent flow has viscosity.
- Laminar flow occurs only in gases; turbulent flow in liquids.
- Reynolds number > 2000 indicates laminar flow.
Answer: In laminar flow, velocity at any point remains constant; in turbulent flow, it varies randomly.
Laminar flow is orderly with layers sliding smoothly, so velocity at a point is constant over time. Turbulent flow is chaotic with random fluctuations in velocity. Viscosity affects both types; both can occur in gases and liquids; Reynolds number > 2000 typically indicates turbulent flow, not laminar.
6. A rubber band is stretched and then released. It returns to its original shape. This behaviour is classified as:
- Plastic behaviour
- Elastic behaviour
- Viscoelastic behaviour
- Brittle behaviour
Answer: Elastic behaviour
Materials that return to their original shape after the deforming force is removed exhibit elastic behaviour. Plastic behaviour involves permanent deformation, viscoelastic behaviour shows time-dependent strain, and brittle behaviour fractures without significant deformation.
7. A block of volume 0.1 m³ is fully immersed in water (density 1000 kg/m³). What is the buoyant force acting on it? (Take g = 10 m/s².)
- 1000 N
- 100 N
- 10 N
- 0.1 N
Answer: 1000 N
Archimedes' principle states buoyant force = weight of displaced fluid = ρ_fluid × V_displaced × g = 1000 kg/m³ × 0.1 m³ × 10 m/s² = 1000 N. The other options are incorrect because they arise from omitting g (100 N), dividing by 10 (10 N), or using volume alone (0.1 N).
8. A wooden block floats in water with two-thirds of its volume submerged. What is the density of the wood relative to water?
- 2/3
- 1/3
- 3/2
- 1
Answer: 2/3
For a floating body, the fraction of volume submerged equals the ratio of the density of the body to the density of the fluid (law of flotation). Here, submerged fraction = 2/3, so relative density = 2/3. Options B, C, and D do not match the given submerged fraction.
9. In a hydraulic lift, the cross-sectional area of the larger piston is 5 times that of the smaller piston. A force of 100 N is applied on the smaller piston. What is the force exerted by the larger piston (ignoring friction)?
- 500 N
- 20 N
- 100 N
- 50 N
Answer: 500 N
According to Pascal's law, the pressure transmitted through the fluid is the same on both pistons: P = F₁/A₁ = F₂/A₂. Given A₂ = 5 A₁, we have F₂ = (A₂/A₁) × F₁ = 5 × 100 N = 500 N. The other options are incorrect because they do not follow the area ratio.
10. On a stress-strain curve for a ductile material, the point up to which the material can withstand stress without permanent deformation is called the:
- Breaking point
- Yield point
- Elastic limit
- Ultimate stress point
Answer: Elastic limit
The elastic limit is the maximum stress a material can endure without permanent deformation. Beyond it, plastic deformation begins. The yield point is where plastic flow starts, breaking point is fracture, and ultimate stress is the maximum stress reached.
11. A venturimeter is used to measure:
- flow speed of a fluid
- viscosity of a fluid
- density of a fluid
- pressure of a fluid
Answer: flow speed of a fluid
A venturimeter works on Bernoulli's principle and the equation of continuity. It measures the flow speed (or flow rate) of a fluid by noting the pressure difference at the constriction. It does not directly measure viscosity, density, or absolute pressure.
12. When a cylindrical rod is subjected to a tangential force parallel to its cross-section, the type of strain produced is called:
- Longitudinal strain
- Volumetric strain
- Shear strain
- Normal strain
Answer: Shear strain
Shear strain occurs when a force is applied parallel to a surface, causing angular distortion. Longitudinal strain involves change in length, volumetric strain involves change in volume, and normal strain is a general term for tensile/compressive strain.