#hydraulic system

Surface Tension, Capillarity and Excess Pressure

A 1500kg car is lifted by a hydraulic system with a small piston of radius 6cm and a large piston of radius 18cm. What f

F1 = A1A2F2, F2 = 1500×9.8 = 14700N. A1 = π(0.06)2, A2 = π(0.18)2, A1A2 = 0.00360.0324 = 19. F1 = 147009 = 1633.33N≈1633N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1633 N. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Viscosity, Stokes' Law and Reynolds Number

What happens if the pressure applied to a hydraulic system exceeds the fluid’s ability to transmit it?

Pascal’s law assumes an incompressible fluid. If pressure exceeds the fluid’s incompressibility limit, the fluid compresses or the system fails (e.g., leaks or bursts), as the assumption of uniform pressure transmission breaks down.

Ref: NCBI Bookshelf, Ideal Gas Law: P1V1/T1 = P2V2/T2.

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Fluid Pressure, Pascal's Law and Manometers

A hydraulic system has a small piston (0.005m2) and a large piston (0.025m2). If 80N is applied on the small piston, wha

Pascal’s law: P = F1A1 = F2A2. F2 = F1×A2A1. F1 = 80N, A1 = 0.005m2, A2 = 0.025m2. F2 = 80×0.0250.005 = 80×5 = 400N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 400 N. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Surface Tension, Capillarity and Excess Pressure

A car lift uses a small piston of radius 4cm to lift a 1200kg car on a piston of radius 12cm. What force is applied on t

F1 = A1A2F2, F2 = mg = 1200×10 = 12000N. A1 = π(0.04)2, A2 = π(0.12)2. A1A2 = (0.04)2(0.12)2 = 0.00160.0144 = 19. F1 = 120009 = 1333.33N≈1333N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 1333 N. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Bernoulli's Theorem and Applications

A hydraulic system applies 180N on a small piston of area 0.012m2. What force is exerted by a large piston of area 0.06m

Pascal’s law: P = F1A1 = F2A2. F2 = F1×A2A1. F1 = 180N, A1 = 0.012m2, A2 = 0.06m2. F2 = 180×0.060.012 = 180×5 = 900N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 900 N. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Equation of Continuity and Flow Rate

A hydraulic system applies 300N on a small piston of area 0.015m2. What force is exerted by a large piston of area 0.045

Pascal’s law: P = F1A1 = F2A2. F2 = F1×A2A1. F1 = 300N, A1 = 0.015m2, A2 = 0.045m2. F2 = 300×0.0450.015 = 300×3 = 900N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 900 N. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Equation of Continuity and Flow Rate

A hydraulic system applies 150N on a small piston of area 0.015m2. What force is exerted by a large piston of area 0.075

Pascal’s law: P = F1A1 = F2A2. F2 = F1×A2A1. F1 = 150N, A1 = 0.015m2, A2 = 0.075m2. F2 = 150×0.0750.015 = 150×5 = 750N. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 750 N. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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