Fluid Mechanics | Surface Tension And Viscosity | JEE Main previous year questions with Solutions

Q 1 :
Mercury is filled in a tube of radius 2 cm up to a height of 30 cm. The force exerted by mercury on the bottom of the tube is ________ N.

$(G i v e n, a t m o s p h e r i c p r e s s u r e = 10^{5}$ $N m^{- 2}, d e n s i t y o f m e r c u r y 1.36 \times 10^{4} k g$ $m^{- 3}, g = 10$ $m s^{- 2}, π = \frac{22}{7})$ [2024]

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(177) $P = P_{0} + ρ g h$

$F = P_{0} A + ρ g h A = \frac{22}{7} \times 4 \times 10^{- 4} (10^{5} + 1.36 \times 10^{4} \times 10 \times \frac{30}{100})$

$\Rightarrow F = \frac{88}{7} \times 10^{- 4} (10^{5} + 0.408 \times 10^{5})$

$= \frac{88}{7} \times 10 \times 1.408 = 177$

Q 2 :
A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of 10 N is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is _________ N. [2024]

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(1000)

$\frac{F_{1}}{A_{1}} = \frac{F_{2}}{A_{2}}$

$\frac{F_{1}}{π {(7)}^{2}} = \frac{10}{π {(0.7)}^{2}} \Rightarrow F_{1} = 1000 N$

Q 3 :
Two cylindrical vessels of equal cross-sectional area of $2 m^{2}$ contain water upto height 10 m and 6 m, respectively. If the vessels are connected at their bottom, then the work done by the force of gravity is: (Density of water is $10^{3} kg / m^{3}$ and $g = 10 m / s^{2}$ ) [2025]

$1 \times 10^{5} J$
$4 \times 10^{4} J$
$6 \times 10^{4} J$
$8 \times 10^{4} J$

1

2

3

4

(4)

$U_{initial} = (ρ A \times 10) g \times 5 + (ρ A 6) g \times 3$

$U_{initial} = ρ A g (50 + 18) = 68 ρ A g$

$U_{final} = (ρ A \times 16) g \times 4 = (ρ A g) \times 64$

$W = △ U = 68 ρ A g - 64 ρ A g = 4 ρ A g$

$W = 4 \times 1000 \times 2 \times 10 = 8 \times 10^{4} J$

Q 4 :
In a hydraulic lift, the surface area of the input piston is 6 ${cm}^{2}$ and that of the output piston is 1500 ${cm}^{2}$ . If 100 N force is applied to the input piston to raise the output piston by 20 cm, then the work done is ______ kJ. [2025]

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(5)

$\frac{F_{1}}{A_{1}} = \frac{F_{2}}{A_{2}}, \frac{100}{6} = \frac{F}{1500}, F = \frac{50}{3} \times 1500$

$F = 50 \times 500 = 25 \times 10^{3} N$

$W = \vec{F} . \vec{S} = 25 \times 10^{3} \times \frac{20}{100} = 5 \times 10^{3} = 5 kJ$

Q 5 :
A vessel wih square cross-section and height of 6 m is vertically partitioned. A small window of 100 ${cm}^{2}$ with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density $1.5 \times 10^{3} kg / m^{3}$ . What force one needs to apply on the hinged door so that it does not get opened? (Acceleration due to gravity = 10 $m / s^{2}$ ) [2025]

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(150)

in equilibrium

$F_{ext} + F_{w} = F_{l}$

$\Rightarrow F_{ext} = F_{l} - F_{w}$

$= (P_{0} + ρ_{l} g h) A - (P_{0} + ρ_{w} g h) A$

$= (ρ_{l} - ρ_{w}) g h A$

$= (1500 - 1000) \times 10 \times 3 \times (100 \times 10^{- 4})$

= 150 N.

Topic Question Set

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Q 2 :
A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of 10 N is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is _________ N. [2024]

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Q 3 :
Two cylindrical vessels of equal cross-sectional area of $2 m^{2}$ contain water upto height 10 m and 6 m, respectively. If the vessels are connected at their bottom, then the work done by the force of gravity is: (Density of water is $10^{3} kg / m^{3}$ and $g = 10 m / s^{2}$ ) [2025]

Q 4 :
In a hydraulic lift, the surface area of the input piston is 6 ${cm}^{2}$ and that of the output piston is 1500 ${cm}^{2}$ . If 100 N force is applied to the input piston to raise the output piston by 20 cm, then the work done is ______ kJ. [2025]

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Topic Question Set

Q 1 : Mercury is filled in a tube of radius 2 cm up to a height of 30 cm. The force exerted by mercury on the bottom of the tube is ________ N. (Given, atmospheric pressure=105 Nm-2,density of mercury 1.36×104kg m-3,g=10 ms-2,π=227) [2024]

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Q 2 : A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of 10 N is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is _________ N. [2024]

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Q 3 : Two cylindrical vessels of equal cross-sectional area of 2 m2 contain water upto height 10 m and 6 m, respectively. If the vessels are connected at their bottom, then the work done by the force of gravity is: (Density of water is 103 kg/m3 and g=10 m/s2) [2025]

Q 4 : In a hydraulic lift, the surface area of the input piston is 6 cm2 and that of the output piston is 1500 cm2. If 100 N force is applied to the input piston to raise the output piston by 20 cm, then the work done is ______ kJ. [2025]

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Q 2 :
A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of 10 N is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is _________ N. [2024]

Q 3 :
Two cylindrical vessels of equal cross-sectional area of $2 m^{2}$ contain water upto height 10 m and 6 m, respectively. If the vessels are connected at their bottom, then the work done by the force of gravity is: (Density of water is $10^{3} kg / m^{3}$ and $g = 10 m / s^{2}$ ) [2025]

Q 4 :
In a hydraulic lift, the surface area of the input piston is 6 ${cm}^{2}$ and that of the output piston is 1500 ${cm}^{2}$ . If 100 N force is applied to the input piston to raise the output piston by 20 cm, then the work done is ______ kJ. [2025]