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JEE Mains | PYQ

Given below are two statements:
Statement I : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water.
Statement II : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water.
In the light of the above statements, choose the most appropriate from the options given below.

Pressure inside a soap bubble is greater than the pressure outside by an amount:
(given: \( R = \) Radius of bubble, \( S = \) Surface tension of bubble)

A small ball of mass \( m \) and density \( \rho \) is dropped in a viscous liquid of density \( \rho_{0} \). After sometime, the ball falls with constant velocity. The viscous force on the ball is:

Small water droplets of radius \( 0.01 \, \text{mm} \) are formed in the upper atmosphere and falling with a terminal velocity of \( 10 \, \text{cm/s} \). Due to condensation, if \( 8 \) such droplets are coalesced and formed a large drop, the new terminal velocity will be _______ \( \text{cm/s} \).

Given below are two statements:
Statement I: The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.
Statement II: The rise of a liquid in a capillary tube does not depend on the inner radius of the tube.
In the light of the above statements, choose the correct answer from the options given below:

Given below are two statements:
Statement I: When speed of liquid is zero everywhere, pressure difference at any two points depends on equation \( P_1 - P_2 = \rho g (h_2 - h_1) \)
Statement II: In ventury tube shown \( 2gh = v_1^2 - v_2^2 \).

In the light of the above statements, choose the most appropriate answer from the options given below:

A plane is in level flight at constant speed and each of its two wings has an area of \( 40 \, \text{m}^2 \). If the speed of the air is \( 180 \, \text{km/h} \) over the lower wing surface and \( 252 \, \text{km/h} \) over the upper wing surface, the mass of the plane is ______ \( \text{kg} \). [Take air density to be \( 1 \, \text{kg m}^{-3} \) and \( g = 10 \, \text{m s}^{-2} \)]

A small spherical ball of radius \( r \), falling through a viscous medium of negligible density has terminal velocity \(' v '\). Another ball of the same mass but of radius \( 2r \), falling through the same viscous medium will have terminal velocity:

A small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity time graph for the transit of the ball?

A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of \( 10 \, \text{N} \) 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 _____ \( \text{N} \).

Given below are two statements :
Statement (I) : Viscosity of gases is greater than that of liquids.
Statement (II) : Surface tension of a liquid decreases due to the presence of insoluble impurities.
In the light of the above statements, choose the most appropriate answer from the options given below :

A liquid column of height \( 0.04 \, \text{cm} \) balances excess pressure of a soap bubble of certain radius. If density of liquid is \( 8 \times 10^{3} \, \text{kg m}^{-3} \) and surface tension of soap solution is \( 0.28 \, \text{N m}^{-1} \), then diameter of the soap bubble is ______ \( \text{cm} \).
[If \( g = 10 \, \text{m s}^{-2} \)]

The radius of pressure metre attached with a closed pipe is \( 4.5 \times 10^{4} \, \text{N}/\text{m}^{2} \). On opening the value, water starts flowing and the reading of pressure metre falls to \( 2.0 \times 10^{4} \, \text{N}/\text{m}^{2} \). The velocity of water is found to be \( \sqrt{V} \, \text{m}/\text{s} \). The value of V is ____________ .

A big drop is formed by coalescing \( 1000 \) small droplets of water. The surface energy will become:

A big drop is formed by coalescing \( 1000 \) small droplets of water. The ratio of surface energy of \( 1000 \) droplets to that of energy of big drop is \( \dfrac{10}{x} \). The value of \( x \) is __________.

Given below are two statements:
Statement I : When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be \( 0^\circ \).
Statement II : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.
In the light of the above statement, choose the correct answer from the options given below:

A small liquid drop of radius \( R \) is divided into \( 27 \) identical liquid drops. If the surface tension is \( T \), then the work done in the process will be:

In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are \( 70 \, \text{m s}^{-1} \) and \( 65 \, \text{m s}^{-1} \) respectively. If the wing area is \( 2 \, \text{m}^2 \), the lift of the wing is __________ N.
(Given density of air \( = 1.2 \, \text{kg m}^{-3} \))

A sphere of relative density \( \sigma \) and diameter \( D \) has concentric cavity of diameter \( d \). The ratio of \( \dfrac{D}{d} \), if it just floats on water in a tank is:

Mercury is filled in a tube of radius \( 2 \, \text{cm} \) up to a height of \( 30 \, \text{cm} \). The force exerted by mercury on the bottom of the tube is _______________ \( \text{N} \).
(Given, atmospheric pressure \( = 10^{5} \, \text{N m}^{-2} \), density of mercury \( = 1.36 \times 10^{4} \, \text{kg m}^{-3} \), \( g = 10 \, \text{m s}^{-2} \), \( \pi = \dfrac{22}{7} \))

A soap bubble is blown to a diameter of \( 7 \) \( \text{cm} \). \( 36960 \) \( \text{erg} \) of work is done in blowing it further. If surface tension of soap solution is \( 40 \) \( \text{dyne/cm} \) then the new radius is _________ \( \text{cm} \). Take \( \left( \pi = \frac{22}{7} \right) \).

Correct Bernoulli’s equation is: [Symbols have their usual meaning]

A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil (specific gravity of Kerosene oil \( = 0.8 \), specific gravity of ice \( = 0.9 \)):