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GATE 2026 ME – Question 29

Fluid Mechanics · Fluid properties, fluid statics, forces on submerged bodies, stability of floating bodies · 1 mark · Multiple choice

A hydraulic crane supports a mass of 500 kg with its piston-cylinder actuator, inclined at 60° with horizontal, as shown in the figure below. The diameter of the piston is 30 cm and gravitational acceleration is 10 m/s$^2$. Neglecting mass of the piston, the reading of the pressure gage in kPa (gage) is

A piston-cylinder actuator filled with oil, inclined at 60° to the horizontal. A 500 kg mass is carried at the top of the piston, and a pressure gage is connected to the oil chamber.
  1. 61.26
  2. 6.13
  3. 35.35
  4. 70.71

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Correct answer: (A) 61.26

Explanation

The piston acts along its own inclined axis, so the force it carries is the component of the weight along that axis: $500 \times 10 \times \sin 60° = 4330$ N. The piston area is $\frac{\pi}{4}(0.3)^2 = 0.0707$ m$^2$. The gauge pressure is $\frac{4330}{0.0707} = 61{,}260$ Pa, which is 61.26 kPa.