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?

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

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:

A wire of length $$L$$ and radius $$r$$ is clamped at one end. If its other end is pulled by a force $$F$$, its length increases by $$l$$. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become:

Young's modules of material of a wire of length '$$L$$' and cross-sectional area $$A$$ is $$Y$$. If the length of the wire is doubled and cross-sectional area is halved then Young's modules will be :

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

A spherical ball of radius $$1\times 10^{-4}\mathrm{m}$$ and density $$10^5\mathrm{kg}/{\mathrm{m}}^3$$ falls freely under gravity through a distance $$h$$ before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value of $$h$$ is approximately: (The coefficient of viscosity of water is $$9.8\times 10^{-6}\mathrm{N}\mathrm{s}/{\mathrm{m}}^2$$)

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

Given below are two statements : Statement I : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation $${\mathrm{P}}_1-{\mathrm{P}}_2=\rho g\left({\mathrm{h}}_2-{\mathrm{h}}_1\right)$$. Statement II : In ventury tube shown $$2\mathrm{gh}=v_1^2-v_2^2$$ In the light of the above statements, choose the most appropriate answer from the options given below.

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 :

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):

Young's modulus is determined by the equation given by $$\mathrm{Y}=49000\frac{\mathrm{m}}{\mathrm{l}}\frac{\mathrm{dyne}}{{\mathrm{cm}}^2}$$ where $$M$$ is the mass and $$l$$ is the extension of wire used in the experiment. Now error in Young modules $$(Y)$$ is estimated by taking data from $$M-l$$ plot in graph paper. The smallest scale divisions are $$5\mathrm{g}$$ and $$0.02\mathrm{cm}$$ along load axis and extension axis respectively. If the value of $M$ and $l$ are $$500\mathrm{g}$$ and $$2\mathrm{cm}$$ respectively then percentage error of $$Y$$ is :

Correct Bernoulli's equation is (symbols have their usual meaning) :

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.

Match List I with List II : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-c3ow{border-color:inherit;text-align:center;vertical-align:top} .tg .tg-7btt{border-color:inherit;font-weight:bold;text-align:center;vertical-align:top} .tg .tg-0pky{border-color:inherit;text-align:left;vertical-align:top} LIST I LIST II A. A force that restores an elastic body of unit area to its original state I. Bulk modulus B. Two equal and opposite forces parallel to opposite faces II. Young's modulus C. Forces perpendicular everywhere to the surface per unit area same everywhere III. Stress D. Two equal and opposite forces perpendicular to opposite faces Choose the correct answer from the options given below : IV. Shear modulus Choose the correct answer from the options given below :

Pressure inside a soap bubble is greater than the pressure outside by an amount : (given : $$\mathrm{R}=$$ Radius of bubble, $$\mathrm{S}=$$ 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 :

A ball of mass $0.5\mathrm{kg}$ is attached to a string of length $50\mathrm{cm}$. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is $400\mathrm{N}$. The maximum possible value of angular velocity of the ball in $\mathrm{rad}/\mathrm{s}$ is, :

A particle moving in a circle of radius $\mathrm{R}$ with uniform speed takes time $\mathrm{T}$ to complete one revolution. If this particle is projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it is equal to $4 R$. The angle of projection $\theta$ is then given by :