Given below are two statements: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathbf{R}$$ Assertion A : A spherical body of radius $$(5\pm 0.1)\mathrm{mm}$$ 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

The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross - section. Cross sectional areas at $$\mathrm{A}$$ is $$1.5{\mathrm{cm}}^2$$, and $$\mathrm{B}$$ is $$25{\mathrm{mm}}^2$$, if the speed of liquid at $$\mathrm{B}$$ is $$60\mathrm{cm}/\mathrm{s}$$ then $$\left({\mathrm{P}}_{\mathrm{A}}-{\mathrm{P}}_{\mathrm{B}}\right)$$ is : (Given $${\mathrm{P}}_{\mathrm{A}}$$ and $${\mathrm{P}}_{\mathrm{B}}$$ are liquid pressures at $$\mathrm{A}$$ and $$\mathrm{B}$$% points. density $$\rho =1000\mathrm{kg}{\mathrm{m}}^{-3}$$ $$\mathrm{A}$$ and $$\mathrm{B}$$ are on the axis of tube

Under isothermal condition, the pressure of a gas is given by $$\mathrm{P}=a{\mathrm{V}}^{-3}$$, where $$a$$ is a constant and $$\mathrm{V}$$ is the volume of the gas. The bulk modulus at constant temperature is equal to

A body cools from $$80^{\circ }\mathrm{C}$$ to $$60^{\circ }\mathrm{C}$$ in 5 minutes. The temperature of the surrounding is $$20^{\circ }\mathrm{C}$$. The time it takes to cool from $$60^{\circ }\mathrm{C}$$ to $$40^{\circ }\mathrm{C}$$ is :

Eight equal drops of water are falling through air with a steady speed of $$10\mathrm{cm}/\mathrm{s}$$. If the drops coalesce, the new velocity is:-

Young's moduli of the material of wires A and B are in the ratio of $$1:4$$, while its area of cross sections are in the ratio of $$1:3$$. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires $$\mathrm{A}$$ and $$\mathrm{B}$$ will be in the ratio of [Assume length of wires A and B are same]

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:

A hydraulic automobile lift is designed to lift vehicles of mass $$5000\mathrm{kg}$$. The area of cross section of the cylinder carrying the load is $$250{\mathrm{cm}}^2$$. The maximum pressure the smaller piston would have to bear is $$[$$ Assume $$g=10\mathrm{m}/{\mathrm{s}}^2]$$

An air bubble of volume $$1{\mathrm{cm}}^3$$ rises from the bottom of a lake $$40\mathrm{m}$$ deep to the surface at a temperature of $$12^{\circ }\mathrm{C}$$. The atmospheric pressure is $$1\times 10^5\mathrm{Pa}$$ the density of water is $$1000\mathrm{kg}/{\mathrm{m}}^3$$ and $$\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$$. There is no difference of the temperature of water at the depth of $$40\mathrm{m}$$ and on the surface. The volume of air bubble when it reaches the surface will be:

An aluminium rod with Young's modulus $$Y=7.0\times 10^{10}\mathrm{N}/{\mathrm{m}}^2$$ undergoes elastic strain of $$0.04\%$$. The energy per unit volume stored in the rod in SI unit is:

A small ball of mass $$\mathrm{M}$$ 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 ?

Given below are two statements: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathbf{R}$$ 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

A stone of mass $1\mathrm{kg}$ is tied to end of a massless string of length $1\mathrm{m}$. If the breaking tension of the string is $400\mathrm{N}$, then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is :

A body is moving with constant speed, in a circle of radius $10\mathrm{m}$. The body completes one revolution in $4\mathrm{s}$. At the end of 3rd second, the displacement of body (in $\mathrm{m}$ ) from its starting point is :

An object moves at a constant speed along a circular path in a horizontal plane with center at the origin. When the object is at $$x=+2\mathrm{m}$$, its velocity is $$-4\hat{\mathrm{j}}$$ m/s. The object's velocity (v) and acceleration (a) at $$x=-2\mathrm{m}$$ will be

A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of car will be, if friction between tyres and road is 0.34. [take g = 10 ms$${}^{-2}$$]

A car is moving with a constant speed of 20 m/s in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take g = 10 m/s$${}^2$$)

A body of mass 200g is tied to a spring of spring constant 12.5 N/m, while the other end of spring is fixed at point O. If the body moves about O in a circular path on a smooth horizontal surface with constant angular speed 5 rad/s. Then the ratio of extension in the spring to its natural length will be :

A vehicle of mass $$200\mathrm{kg}$$ is moving along a levelled curved road of radius $$70\mathrm{m}$$ with angular velocity of $$0.2\mathrm{rad}/\mathrm{s}$$. The centripetal force acting on the vehicle is:

A coin placed on a rotating table just slips when it is placed at a distance of $$1\mathrm{cm}$$ from the center. If the angular velocity of the table in halved, it will just slip when placed at a distance of _________ from the centre :