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In a car lift, compressed air exerts a force F1 on a small piston having a radius of 5cm. This pressure is transmitted to the second piston of a radius of 15cm. If the mass of the car to be lifted is 1350 kg. What is F1?
- a)14.7 * 103 N
- b)2.47 * 103 N
- c)1.47 * 103 N
- d)24.7 * 103 N
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
In a car lift, compressed air exerts a forceF1on a small piston having...
Understanding the Problem
In a hydraulic lift system, the force exerted on one piston is transmitted to another piston. This principle is based on Pascal's law, which states that pressure applied to a confined fluid is transmitted undiminished throughout the fluid.
Given Data
- Radius of the small piston (r1) = 5 cm = 0.05 m
- Radius of the large piston (r2) = 15 cm = 0.15 m
- Mass of the car (m) = 1350 kg
Calculating the Force on the Large Piston
To lift the car, we first need to calculate the force (F2) acting on the larger piston due to the weight of the car:
- Weight of the car (F2) = m * g
- Where g = 9.81 m/s² (acceleration due to gravity)
Calculating F2:
- F2 = 1350 kg * 9.81 m/s² = 13243.5 N (approximately 13245 N)
Using the Hydraulic Principle
The pressure exerted on both pistons is equal:
- Pressure (P) = Force (F) / Area (A)
The area A can be calculated as:
- A1 = π * (r1)² for the small piston
- A2 = π * (r2)² for the large piston
Calculating areas:
- A1 = π * (0.05)² = 0.00785 m²
- A2 = π * (0.15)² = 0.07069 m²
Equating Pressures
Now, set the pressures equal:
- F1 / A1 = F2 / A2
Solving for F1 gives us:
- F1 = F2 * (A1 / A2)
Substituting the values:
- F1 = 13245 N * (0.00785 m² / 0.07069 m²) = 1470 N (approximately 1.47 * 10^3 N)
Conclusion
Thus, the required force F1 is approximately 1.47 * 10^3 N, confirming that option 'C' is indeed correct.
In a hydraulic lift system, the force exerted on one piston is transmitted to another piston. This principle is based on Pascal's law, which states that pressure applied to a confined fluid is transmitted undiminished throughout the fluid.
Given Data
- Radius of the small piston (r1) = 5 cm = 0.05 m
- Radius of the large piston (r2) = 15 cm = 0.15 m
- Mass of the car (m) = 1350 kg
Calculating the Force on the Large Piston
To lift the car, we first need to calculate the force (F2) acting on the larger piston due to the weight of the car:
- Weight of the car (F2) = m * g
- Where g = 9.81 m/s² (acceleration due to gravity)
Calculating F2:
- F2 = 1350 kg * 9.81 m/s² = 13243.5 N (approximately 13245 N)
Using the Hydraulic Principle
The pressure exerted on both pistons is equal:
- Pressure (P) = Force (F) / Area (A)
The area A can be calculated as:
- A1 = π * (r1)² for the small piston
- A2 = π * (r2)² for the large piston
Calculating areas:
- A1 = π * (0.05)² = 0.00785 m²
- A2 = π * (0.15)² = 0.07069 m²
Equating Pressures
Now, set the pressures equal:
- F1 / A1 = F2 / A2
Solving for F1 gives us:
- F1 = F2 * (A1 / A2)
Substituting the values:
- F1 = 13245 N * (0.00785 m² / 0.07069 m²) = 1470 N (approximately 1.47 * 10^3 N)
Conclusion
Thus, the required force F1 is approximately 1.47 * 10^3 N, confirming that option 'C' is indeed correct.
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Community Answer
In a car lift, compressed air exerts a forceF1on a small piston having...
From Pascal’s law:
P1 = P2
F1/A1 = F2/A2
F1/A1 = F2/A2
► F1/πr12 = F
► F1 = (F2 * r12 ) / r22
► F1 = 1350 * 9.8 * (5 * 10-2)2 / (15 * 10-2)2
► F1 = 1470N = 1.47 * 103N
2
/πr22 ► F1 = (F2 * r12 ) / r22
► F1 = 1350 * 9.8 * (5 * 10-2)2 / (15 * 10-2)2
► F1 = 1470N = 1.47 * 103N
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In a car lift, compressed air exerts a forceF1on a small piston having a radius of5cm. This pressure is transmitted to the second piston of a radius of 15cm. If the mass of the car to be lifted is1350kg. What isF1?a)14.7 * 103Nb)2.47 * 103Nc)1.47 * 103Nd)24.7 * 103NCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a car lift, compressed air exerts a forceF1on a small piston having a radius of5cm. This pressure is transmitted to the second piston of a radius of 15cm. If the mass of the car to be lifted is1350kg. What isF1?a)14.7 * 103Nb)2.47 * 103Nc)1.47 * 103Nd)24.7 * 103NCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a car lift, compressed air exerts a forceF1on a small piston having a radius of5cm. This pressure is transmitted to the second piston of a radius of 15cm. If the mass of the car to be lifted is1350kg. What isF1?a)14.7 * 103Nb)2.47 * 103Nc)1.47 * 103Nd)24.7 * 103NCorrect answer is option 'C'. Can you explain this answer?.
In a car lift, compressed air exerts a forceF1on a small piston having a radius of5cm. This pressure is transmitted to the second piston of a radius of 15cm. If the mass of the car to be lifted is1350kg. What isF1?a)14.7 * 103Nb)2.47 * 103Nc)1.47 * 103Nd)24.7 * 103NCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a car lift, compressed air exerts a forceF1on a small piston having a radius of5cm. This pressure is transmitted to the second piston of a radius of 15cm. If the mass of the car to be lifted is1350kg. What isF1?a)14.7 * 103Nb)2.47 * 103Nc)1.47 * 103Nd)24.7 * 103NCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a car lift, compressed air exerts a forceF1on a small piston having a radius of5cm. This pressure is transmitted to the second piston of a radius of 15cm. If the mass of the car to be lifted is1350kg. What isF1?a)14.7 * 103Nb)2.47 * 103Nc)1.47 * 103Nd)24.7 * 103NCorrect answer is option 'C'. Can you explain this answer?.
Solutions for In a car lift, compressed air exerts a forceF1on a small piston having a radius of5cm. This pressure is transmitted to the second piston of a radius of 15cm. If the mass of the car to be lifted is1350kg. What isF1?a)14.7 * 103Nb)2.47 * 103Nc)1.47 * 103Nd)24.7 * 103NCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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