A hydraulic press has a ram of cross-section area 30 cm × 30 cm and a plunger of cross-section area 4 cm × 4 cm. Find the force F required to lift the weight W = 30 kN.
Try it first: pick an option, then read the explanation.
Asked in SSC JE 04/12/2023 (09am-11am)
Detailed Explanation
A hydraulic press operates on Pascal's principle: pressure applied to an enclosed, stationary liquid is transmitted equally and undiminished in all directions throughout the liquid. This produces a mechanical advantage equal to the ratio of ram area to plunger area.
Ram area \(A_1\) and plunger area \(A_2\):
\[ A_1 = 30\text{ cm} \times 30\text{ cm} = 900\text{ cm}^2 \]
\[ A_2 = 4\text{ cm} \times 4\text{ cm} = 16\text{ cm}^2 \]
Applying Pascal's law (\(p_1 = p_2\)):
\[ \frac{W}{A_1} = \frac{F}{A_2} \;\implies\; F = W \times \frac{A_2}{A_1} \]
\[ F = 30 \times 10^3\text{ N} \times \frac{16}{900} = \frac{480{,}000}{900} \approx 533.33\text{ N} \]
Why “533.33 N” Is Correct
Equating the hydrostatic pressure under the ram to the pressure under the plunger yields F = 30,000 N × (16 / 900) = 533.33 N, matching option (b).
Why the Other Options Are Wrong
- A. 589.58 N: 589.58 N is obtained if an erroneous area ratio or incorrect side conversion is used.
- C. 481.22 N: 481.22 N results from an arithmetic error in dividing the areas.
- D. 232.88 N: 232.88 N corresponds to using linear dimension ratios (4/30) instead of area ratios (4/30)².
Key Point
Pascal's law for hydraulic press: F / a = W / A ⇒ F = W(a / A).
Key Concepts for Students
- Pascal's principle: pressure in a confined static fluid is transmitted uniformly without loss.
- Mechanical advantage = Area of ram / Area of plunger = 900 / 16 = 56.25.
- Work done is conserved in an ideal press: F × d_plunger = W × d_ram.
Practice more: this is question 9 in Properties of Fluid MCQs – Part 1. Try the whole set and check every answer instantly.