Two syringes of different cross sections (without needle) filled with water are connected with a tightly fitted rubber tube filled with water. Diameters of the smaller and larger piston are 1 cm and 3 cm respectively. If a force of 10 N is applied to the smaller piston then the force exerted on the larger piston is:

• A. 30 N
• B. 60 N
• C. 90 N
• D. 100 N

To solve this problem, we can use Pascal's principle, which states that pressure applied to a confined fluid is transmitted undiminished throughout the fluid. The pressure exerted on the smaller piston will equal the pressure exerted on the larger piston.

Calculating Pressure

Pressure is defined as force divided by area:

• Pressure on smaller piston: P1 = F1 / A1
• Pressure on larger piston: P2 = F2 / A2

Finding Areas

The area of a circle is calculated using the formula A = πr². Let's find the areas of both pistons:

• Radius of smaller piston (1 cm): r1 = 0.5 cm = 0.005 m
• Area of smaller piston: A1 = π(0.005)² ≈ 7.85 × 10⁻⁵ m²
• Radius of larger piston (3 cm): r2 = 1.5 cm = 0.015 m
• Area of larger piston: A2 = π(0.015)² ≈ 7.07 × 10⁻⁴ m²

Applying Pascal's Principle

Since P1 = P2, we can set up the equation:

F1 / A1 = F2 / A2

Substituting the known values:

10 N / (7.85 × 10⁻⁵ m²) = F2 / (7.07 × 10⁻⁴ m²)

Solving for F2

Cross-multiplying gives:

F2 = (10 N) × (7.07 × 10⁻⁴ m²) / (7.85 × 10⁻⁵ m²)

Calculating this results in:

F2 ≈ 90 N

Final Answer

The force exerted on the larger piston is 90 N, so the correct option is C. 90 N.