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JEE Mains | PYQ

A water drop of radius \( 1 \, \text{cm} \) is broken into \( 729 \) equal droplets. If surface tension of water is \( 75 \, \text{dyne}/\text{cm} \), then the gain in surface energy upto first decimal place will be:
(Given \( \pi = 3.14 \))

If \( \rho \) is the density and \( \eta \) is coefficient of viscosity of fluid which flows with a speed \( v \) in the pipe of diameter \( d \), the correct formula for Reynolds number \( R_{e} \) is:

The area of cross-section of a large tank is \( 0.5 \, \text{m}^{2} \). It has a narrow opening near the bottom having area of cross-section \( 1 \, \text{cm}^{2} \). A load of \( 25 \, \text{kg} \) is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is \( 40 \, \text{cm} \) above the bottom, will be ________ \( \text{cm s}^{-1} \). [Take \( g = 10 \, \text{m s}^{-2} \)]

The velocity of a small ball of mass ‘\( m \)’ and density \( d_1 \), when dropped in container filled with glycerine, becomes constant after some time. If the density of glycerine is \( d_2 \), then the viscous force acting on the ball, will be:

A tube of length \( 50 \, \text{cm} \) is filled completely with an incompressible liquid of mass \( 250 \, \text{g} \) and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity \( x\sqrt{F} \) \( \text{rad s}^{-1} \). If \( F \) be the force exerted by the liquid at the other end then the value of \( x \) will be _______.

A liquid of density \( 750\,\text{kg m}^{-3} \) flows smoothly through a horizontal pipe that tapers in cross-sectional area from \( A_1 = 1.2 \times 10^{-2}\,\text{m}^2 \) to \( A_2 = \frac{A_1}{2} \). The pressure difference between the wide and narrow sections of the pipe is \( 4500\,\text{Pa} \). The rate of flow of liquid is ____________ \( \times 10^{-3}\,\text{m}^3\text{s}^{-1} \).

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Clothes containing oil or grease stains cannot be cleaned by water wash.
Reason (R): Because the angle of contact between the oil/grease and water is obtuse.
In the light of the above statements, choose the correct answer from the option given below:

The diameter of an air bubble which was initially \( 2 \, \text{mm} \), rises steadily through a solution of density \( 1750 \, \text{kg m}^{-3} \) at the rate of \( 0.35 \, \text{cms}^{-1} \). The coefficient of viscosity of the solution is ______ poise (in nearest integer). (the density of air is negligible).

A drop of liquid of density \( \rho \) is floating half immersed in a liquid of density \( \sigma \) and surface tension \( 7.5 \times 10^{-4} \, \text{N cm}^{-1} \). The radius of drop in cm will be: \( ( g = 10 \, \text{ms}^{-2} ) \)

An ideal fluid of density \( 800 \,\mathrm{kg\, m^{-3}} \), flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from \( a \) to \( \frac{a}{2} \). The pressure difference between the wide and narrow sections of pipe is \( 4100 \,\mathrm{Pa} \). At wider section, the velocity of fluid is \( \frac{\sqrt{x}}{6} \,\mathrm{m\, s^{-1}} \) for \( x = \) ____________. (Given \( g = 10 \,\mathrm{m\, s^{-2}} \) )

The terminal velocity \( (v_t) \) of the spherical rain drop depends on the radius \( (r) \) of the spherical rain drop as: