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A liquid drop of diameter \( 2 \, \text{mm} \) breaks into \( 512 \) droplets. The change in surface energy is \( \alpha \times 10^{-6} \, \text{J} \). The value of \( \alpha \) is ______. (Take surface tension of liquid = \( 0.08 \, \text{N/m} \))

A soap bubble of surface tension \( 0.04 \, \text{N/m} \) is blown to a diameter of \( 7 \, \text{cm} \). If \( (15000 - x) \, \mu \text{J} \) of work is done in blowing it further to make its diameter \( 14 \, \text{cm} \), then the value of \( x \) is ____________ . \( \left( \pi = \dfrac{22}{7} \right) \).

A cubical block of density \( \rho_b = 600 \, \text{kg/m}^3 \) floats in a liquid of density \( \rho_e = 900 \, \text{kg/m}^3 \). If the height of block is \( H = 8.0 \, \text{cm} \) then height of the submerged part is ________________ \( \text{cm} \).

A liquid of density \( 600 \, \text{kg} \, \text{m}^{-3} \) flowing steadily in a tube of varying cross-section. The cross-section at a point A is \( 1.0 \, \text{cm}^2 \) and that at B is \( 20 \, \text{mm}^2 \). Both the points A and B are in same horizontal plane, the speed of the liquid at A is \( 10 \, \text{cm} \, \text{s}^{-1} \). The difference in pressures at A and B points is ______ \( \text{Pa} \).

Surface tension of two liquids (having same densities), \( T_1 \) and \( T_2 \), are measured using capillary rise method utilizing two tubes with inner radii of \( r_1 \) and \( r_2 \) where \( r_1 > r_2 \). The measured liquid heights in these tubes are \( h_1 \) and \( h_2 \) respectively. [Ignore the weight of the liquid about the lowest point of meniscus]. The heights \( h_1 \) and \( h_2 \) and surfaces tensions \( T_1 \) and \( T_2 \) satisfy the relation:

A spherical liquid drop of radius \( R \) acquires the terminal velocity \( v_1 \) when falls through a gas of viscosity \( \eta \). Now the drop is broken into \( 64 \) identical droplets and each droplet acquires terminal velocity \( v_2 \) falling through the same gas. The ratio of terminal velocities \( \dfrac{v_1}{v_2} \) is ______.

Given below are two statements:
Statement I: Pressure of a fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid.
Statement II: Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension.
In the light of the above statements, choose the correct answer from the options given below

Sixty four rain drops of radius \( 1 \, \text{mm} \) each falling down with a terminal velocity of \( 10 \, \text{cm/s} \) coalesce to form a bigger drop. The terminal velocity of bigger drop is ______ \( \text{cm/s} \)

A cylindrical block of mass \( M \) and area of cross section \( A \) is floating in a liquid of density \( \rho \) and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is _______.

Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is \( 5 \, \text{cm} \) and the area of cross-sections at A and B are \( 6 \, \text{cm}^{2} \) and \( 3 \, \text{cm}^{2} \) respectively. The rate of flow will be ______________ \( \text{cm}^{3} / \text{s} \). \( \text{(take } g = 10 \, \text{m} / \text{s}^{2} \text{)} \)

A water spray gun is attached to a hose of cross sectional area \( 30 \, \text{cm}^2 \). The gun comprises of \( 10 \) perforations each of cross sectional area of \( 15 \, \text{mm}^2 \). If the water flows in the hose with the speed of \( 50 \, \text{cm/s} \), calculate the speed at which the water flows out from each perforation. (Neglect any edge effects)

When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height \( h \). If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by \(1\%\) each, then the height of the liquid in the tube will change by ________ \(\%\).

A tub is filled with water and a wooden cube \( 10 \, \text{cm} \times 10 \, \text{cm} \times 10 \, \text{cm} \) is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by \( 3.87 \, \text{cm} \). The mass of the metal coin is ______ gram. (Take water density as \( 1 \, \text{g}/\text{cm}^3 \) and density of wood as \( 0.4 \, \text{g}/\text{cm}^3 \))

The surface tension of a soap solution is \( 3.5\times 10^{-2} \, \text{N} / \text{m} \). The work required to increase the radius of a soap bubble from \( 1 \, \text{cm} \) to \( 2 \, \text{cm} \) is \( \alpha \times 10^{-6} \, \text{J} \). The value of \( \alpha \) is ______. \( \left( \pi=\dfrac{22}{7} \right) \)

The terminal velocity of a metallic ball of radius \( 6 \, \text{mm} \) in a viscous fluid is \( 20 \, \text{cm/s} \). The terminal velocity of another ball of same material and having radius \( 3 \, \text{mm} \) in the same fluid will be ______ \( \text{cm/s} \).

A small metallic sphere of diameter \( 2 \, \text{mm} \) and density \( 10.5 \, \text{g/cm}^3 \) is dropped in glycerine having viscosity \( 10 \, \text{Poise} \) and density \( 1.5 \, \text{g/cm}^3 \) respectively. The terminal velocity by the sphere is ______ \( \text{cm/s} \).
\( (\pi = \frac{22}{7} \text{ and } g = 10 \, \text{m/s}^2) \)

A cylindrical vessel of \( 40 \, \text{cm} \) radius is completely filled with water and its capacity is \( 528 \, \text{dm}^3 \) \( (\text{dm} : \) decimeter\() \). The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at \( 70 \, \text{cm} \) below the top of water level, the horizontal range of water falling on the ground in the beginning is ______ \( \text{cm} \).

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JEE MAIN 2026 24TH Jan Morning Shift

Sixty four rain drops of radius \( 1 \, \text{mm} \) each falling down with a terminal velocity of \( 10 \, \text{cm/s} \) coalesce to form a bigger drop. The terminal velocity of bigger drop is ______ \( \text{cm/s} \)