Grade 11 : Physics - Fluids (Set 1)

Explanation:Pressure is defined as force per unit area: $P = \frac{F}{A} = \frac{50\text{ N}}{0.1m^2} = 500\text{ Pa}$. Hence, option B is correct.

Explanation:The SI unit of pressure is the Pascal (Pa), which is equal to $1\text{ N/m}^2$.

Explanation:Gauge pressure at depth $h$ is $P_g = \rho g h = 1000 \times 9.8 \times 5 = 49000\text{ Pa} = 49\text{ kPa}$.

Explanation:Pascal's Law states that pressure applied to an enclosed fluid is transmitted undiminished throughout the fluid, which is the operational principle of hydraulic lifts.

Explanation:By Pascal's Law, $\frac{F_1}{A_1} = \frac{F_2}{A_2}$. Rearranging gives $F_2 = F_1 \left(\frac{A_2}{A_1}\right) = 100 \times \left(\frac{0.5}{0.02}\right) = 100 \times 25 = 2500\text{ N}$.

Explanation:Archimedes' principle states that the upward buoyant force on an object submerged in a fluid equals the weight of the fluid displaced by the object.

Explanation:Buoyant force $F_b = \rho V g = 1000 \times 0.002 \times 9.8 = 19.6\text{ N}$.

Explanation:Specific Gravity = $\frac{\text{Density of substance}}{\text{Density of water}} = \frac{2700}{1000} = 2.7$.

Explanation:By the equation of continuity, $A_1 v_1 = A_2 v_2 \implies 0.04 \times 2 = 0.01 \times v_2 \implies v_2 = 8m/s$.

Explanation:Bernoulli's equation represents the conservation of mechanical energy per unit volume for an ideal moving fluid.

Explanation:By Torricelli's Law, $v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 5} = \sqrt{98} \approx 9.9m/s$.

Explanation:The SI unit of dynamic viscosity is Pascal-second ($\text{Pa}\cdot\text{s}$), which equals $\text{N}\cdot\text{s/m}^2$.

Explanation:At terminal velocity, downward weight is balanced by upward buoyancy and viscous drag force, yielding net force zero and zero acceleration.

Explanation:Stokes' Law specifies that viscous resistive force $F = 6\pi \eta r v$ for a sphere moving slowly through a fluid.

Explanation:Surface tension $T$ is defined as the force per unit length ($T = F/L$) acting perpendicular to a line drawn on the surface of the liquid.

Explanation:Surface tension is force per unit length, so its SI unit is Newton per meter ($\text{N/m}$), equivalent to $\text{J/m}^2$.

Explanation:Excess pressure inside a liquid drop with one surface is $\Delta P = \frac{2T}{R} = \frac{2 \times 0.07}{0.001} = 140\text{ Pa}$.

Explanation:A soap bubble has two liquid-air surfaces, so excess pressure is $\Delta P = \frac{4T}{R} = \frac{4 \times 0.03}{0.002} = 60\text{ Pa}$.

Explanation:Capillary rise formula is $h = \frac{2T \cos\theta}{\rho g r}$. Height $h$ is inversely proportional to radius $r$. Halving $r$ doubles $h$.

Explanation:Fluid flow is steady and laminar when Reynolds number $N_R < 2000$. For $N_R > 3000$, flow becomes turbulent.