A piston of a cross-sectional area of 100 cm2 is used in a hydraulic press to exert a force of 107 dynes on the water. The cross-sectional area of the other piston which supports an object having a mass of 2000 kg is:
Correct answer: C. 2 x 10^4 cm2
- A. 100 cm2
- B. 109 cm2
- C. 2 x 10^4 cm2
- D. 2 x 10^10cm2
Explanation
The problem involves a hydraulic press, which operates on Pascal's Law: the pressure applied to a confined fluid is transmitted undiminished in all directions. Given that the first piston applies a force of 107 dynes over 100 cm2, the pressure can be calculated as P = F/A = 107 dynes / 100 cm2. This pressure is transmitted to the second piston, which must support a mass of 2000 kg (corresponding to a force due to gravity of approximately 2 × 108 dynes). Solving for the area using A = F/P gives 2 × 104 cm2, making option C correct.P₁ = P₂ ⇒ F₁/A₁ = F₂/A₂⇒ 10⁷/10² = 2000 × 10³ × 10³ / A₂∴ A₂ = 2 × 10⁴ cm² (g = 980 ≈ 10³ cm/s²)Options A and B do not account for the mass and resulting force, while option D is an impractical overestimation.
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