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Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: When you squeeze one end of a tube to get toothpaste out from the other end, Pascal’s principle is observed.
Reason R: A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container.
In the light of the above statements, choose the most appropriate answer from the options given below

An air bubble of diameter \( 6 \, \text{mm} \) rises steadily through a solution of density \( 1750 \, \text{kg} / \text{m}^3 \) at the rate of \( 0.35 \, \text{cm}/\text{s} \). The co-efficient of viscosity of the solution (neglect density of air) is ________ \( \text{Pas} \).
(Given, \( g = 10 \, \text{m}\,\text{s}^{-2} \) )

A small ball of mass \( M \) and density \( \rho \) is dropped in a viscous liquid of density \( \rho_{0} \). After some time, the ball falls with a constant velocity. What is the viscous force on the ball?

There is an air bubble of radius \( 1.0 \, \text{mm} \) in a liquid of surface tension \( 0.075 \, \text{N m}^{-1} \) and density \( 1000 \, \text{kg m}^{-3} \) at a depth of \( 10 \, \text{cm} \) below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is ________ \( \text{Pa} \) \( \left( g = 10 \, \text{m s}^{-2} \right) \)

The height of liquid column raised in a capillary two of certain radius when dipped in liquid \( A \) vertically is, \( 5 \, \text{cm} \). If the tube is dipped in a similar manner in another liquid \( B \) of surface tension and density double the values of liquid \( A \), the height of liquid column raised in liquid \( B \) would be _______ \( \text{m} \).

A spherical ball of radius \( 1 \, \text{mm} \) and density \( 10.5 \, \text{g/cc} \) is dropped in glycerin of coefficient of viscosity \( 9.8 \) poise and density \( 1.5 \, \text{g/cc} \). Viscous force on the ball when it attains constant velocity is: \( 3696 \times 10^{-x} \, \text{N} \). The value of \( x \) is: (Given, \( g = 9.8 \, \text{m/s}^2 \) and \( \pi = \frac{22}{7} \))

If \( 1000 \) droplets of water of surface tension \( 0.07 \, \text{N/m} \), having same radius \( 1 \, \text{mm} \) each, combine to from a single drop. In the process the released surface energy is: (Take \( \pi = \frac{22}{7} \))

Given below are two statements:
Statement I : Pressure in a reservoir of water is same at all points at the same level of water.
Statement II: The pressure applied to enclosed water is transmitted in all directions equally.
In the light of the above statements, choose the correct answer from the options given below:

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : A spherical body of radius \( (5 \pm 0.1) \, \text{mm} \) having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is \( 4\% \).
Reason R : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius.
In the light of the above statements, choose the correct answer from the options given below:

A mercury drop of radius \( 10^{-3} \, \text{m} \) is broken into \( 125 \) equal size droplets. Surface tension of mercury is \( 0.45 \, \text{N m}^{-1} \). The gain in surface energy is:

A spherical drop of liquid splits into \( 1000 \) identical spherical drops. If \( u_i \) is the surface energy of the original drop and \( u_f \) is the total surface energy of the resulting drops, the (ignoring evaporation), \( \dfrac{u_f}{u_i} = \left( \dfrac{10}{x} \right) \). Then value of \( x \) is ________.

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JEE Main 2023 6th April Morning Shift

A small ball of mass \( M \) and density \( \rho \) is dropped in a viscous liquid of density \( \rho_{0} \). After some time, the ball falls with a constant velocity. What is the viscous force on the ball?