Fluid Pressure — Important Questions

Transmitted undiminished to every part of the fluid

Step 1: Pascal's Law is a fundamental principle about enclosed fluids. Step 2: When pressure is applied to any part of an enclosed fluid, it is transmitted equally and undiminished to all other parts of the fluid. Step 3: This means every part of the fluid — top, bottom, sides — experiences the same change in pressure. Step 4: This is why when you squeeze one end of a filled water bottle, every side bulges out equally. The other options describe incorrect transmission of pressure.

1000 N

Step 1: By Pascal's Law, pressure is transmitted equally. So pressure at small piston = pressure at large piston. Step 2: Pressure at small piston = F₁/A₁ = 20 N / 2 cm² = 10 N/cm². Step 3: Force on large piston F₂ = Pressure × A₂ = 10 N/cm² × 100 cm² = 1000 N. Step 4: This shows the power of hydraulic systems — a small force of 20 N produces a large force of 1000 N. Option 500 N would result from using half the area (50 cm²). Option 20 N ignores the area multiplication.

Perpendicular to the surface (normal)

Step 1: Consider a fluid at rest in contact with a surface. Step 2: If there were any tangential (parallel) component of force on the surface, by Newton's 3rd law the surface would exert a tangential force back on the fluid. Step 3: A tangential force would cause the fluid to flow, which contradicts our assumption that the fluid is at rest. Step 4: Therefore, the force exerted by a fluid at rest must be purely perpendicular (normal) to the surface. This is a fundamental property of fluids at rest.

[M L⁻¹ T⁻²]

Step 1: Pressure = Force / Area. Step 2: Dimension of Force = [M L T⁻²] (from F = ma). Step 3: Dimension of Area = [L²]. Step 4: Dimension of Pressure = [M L T⁻²] / [L²] = [M L⁻¹ T⁻²]. The negative exponent on L shows pressure decreases with increasing area. Option [M L T⁻²] is force, [M L² T⁻²] is energy/work, and [M L T⁻¹] is momentum.