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A tube of length \( L \) is shown in the figure. The radius of cross section at the point \( (1) \) is \( 2 \, \text{cm} \) and at the point \( (2) \) is \( 1 \, \text{cm} \), respectively. If the velocity of water entering at point \( (1) \) is \( 2 \, \text{m/s} \), then velocity of water leaving the point \( (2) \) will be:

A capillary tube of radius \( 0.1\,\text{mm} \) is partly dipped in water (surface tension \( 70\,\text{dyn}/\text{cm} \) and glass water contact angle \( =0^\circ \)) with \( 30^\circ \) inclined with the vertical. The length of water risen in capillary is ______ cm. (Take \( g=9.8\,\text{m}/\text{s}^2 \))

The increase in pressure required to decrease the volume of a water sample by \( 0.2\% \) is \( P \times 10^{5} \, \text{N m}^{-2} \). Bulk modulus of water is \( 2.15 \times 10^{9} \, \text{N m}^{-2} \). The value of \( P \) is __________.

The amount of work done to break a big water drop of radius \( 'R' \) into \( 27 \) small drops of equal radius is \( 10 \, \text{J} \). The work required to break the same big drop into \( 64 \) small drops of equal radius will be:

Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is \( P_1 \). The reading of the pressure gauge falls to \( P_2 \) when the valve is opened. The speed of water flowing in the pipe is proportional to:

Two liquids \( A \) and \( B \) have \( \theta_A \) and \( \theta_B \) as contact angles in a capillary tube. If \( K = \cos \theta_A / \cos \theta_B \), then identify the correct statement:

Consider a completely full cylindrical water tank of height \( 1.6 \, \text{m} \) and of cross-sectional area \( 0.5 \, \text{m}^{2} \). It has a small hole in its side at a height \( 90 \, \text{cm} \) from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load \( 50 \, \text{kg} \) is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is: \( (g = 10 \, \text{m}/\text{s}^{2}) \)

In the experiment for measurement of viscosity '\( \eta \)' of given liquid with a ball having radius \( R \), consider following statements.
A. Graph between terminal velocity \( V \) and \( R \) will be a parabola.
B. The terminal velocities of different diameter balls are constant for a given liquid.
C. Measurement of terminal velocity is dependent on the temperature.
D. This experiment can be utilized to assess the density of a given liquid.
E. If balls are dropped with some initial speed, the value of \( \eta \) will change.
Choose the correct answer from the options given below:

A small rigid spherical ball of mass \( M \) is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider \( g \) as acceleration due to gravity)

Given below are two statements:
Statement I: The hot water flows faster than cold water.
Statement II: Soap water has higher surface tension as compared to fresh water.
In the light above statements, choose the correct answer from the options given below:

A cube having a side of \( 10 \, \text{cm} \) with unknown mass and \( 200 \, \text{gm} \) mass were hung at two ends of an uniform rigid rod of \( 27 \, \text{cm} \) long. The rod along with masses was placed on a wedge keeping the distance between wedge point and \( 200 \, \text{gm} \) weight as \( 25 \, \text{cm} \). Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water. (Take the density of unknown mass is more than that of the water, the mass did not absorb water and water density is \( 1 \, \text{gm}/\text{cm}^3 \)). The unknown mass is ______ kg.

An air bubble of radius \( 0.1 \, \text{cm} \) lies at a depth of \( 20 \, \text{cm} \) below the free surface of a liquid of density \( 1000 \, \text{kg/m}^3 \). If the pressure inside the bubble is \( 2100 \, \text{N/m}^2 \) greater than the atmospheric pressure, then the surface tension of the liquid in SI unit is (use \( g = 10 \, \text{m/s}^2 \)).

A vessel with square cross-section and height of \( 6 \, \text{m} \) is vertically partitioned. A small window of \( 100 \, \text{cm}^2 \) with hinged door is fitted at a depth of \( 3 \, \text{m} \) 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 \( 1.5 \times 10^3 \, \text{kg} / \text{m}^3 \). What force one needs to apply on the hinged door so that it does not get opened?
(Acceleration due to gravity \( = 10 \, \text{m} / \text{s}^2 \))

Two soap bubbles of radius \( 2 \, \text{cm} \) and \( 4 \, \text{cm} \), respectively, are in contact with each other. The radius of curvature of the common surface, in \( \text{cm} \), is _________.

In a hydraulic lift, the surface area of the input piston is \( 6 \, \text{cm}^2 \) and that of the output piston is \( 1500 \, \text{cm}^2 \). If \( 100 \, \text{N} \) force is applied to the input piston to raise the output piston by \( 20 \, \text{cm} \), then the work done is __________ kJ.

A tube of length \( 1 \, \text{m} \) is filled completely with an ideal liquid of mass \( 2M \), and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is \( F \) then angular velocity of the tube is \( \sqrt{\frac{F}{\alpha M}} \) in SI unit. The value of \( \alpha \) is __________.

The excess pressure inside a soap bubble \( A \) in air is half the excess pressure inside another soap bubble \( B \) in air. If the volume of the bubble \( A \) is \( n \) times the volume of the bubble \( B \), then, the value of \( n \) is __________.

Consider following statements:
A. Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface, of a liquid.
B. As the temperature of liquid rises, the coefficient of viscosity increases.
C. As the temperature of gas increases, the coefficient of viscosity increases.
D. The onset of turbulence is determined by Reynold’s number.
E. In a steady flow two stream lines never intersect.

Two water drops each of radius ‘\( r \)’ coalesce to form a bigger drop. If ‘\( T \)’ is the surface tension, the surface energy released in this process is:

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JEE Main 2025 22nd Jan Morning Shift

Two soap bubbles of radius \( 2 \, \text{cm} \) and \( 4 \, \text{cm} \), respectively, are in contact with each other. The radius of curvature of the common surface, in \( \text{cm} \), is _________.