JEE Properties of Solids and Liquids PYQs with Solutions PDF

A spherical body of radius r and density $$\sigma$$ falls freely through a viscous liquid having density $$\rho$$ and viscosity $$\eta$$ and attains a terminal velocity $$\upsilon_{0}$$. Estimated maximum error in the quantity $$\eta$$ is: (Ignore errors associated with $$\sigma,\rho$$ and g, gravitational acceleration)

The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 cm/s. The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be ________ cm/ s.

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

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 mm each falling down w-ith a terminal velocity of 10 cm/s coalesce to fonn a bigger drop. The terminal velocity of bigger drop is_____cm/s

A cubical block of density $$\rho_{b}= 600kg/m^{3}$$ floats in a liquid of density $$\rho_{e}= 900kg/m^{3}$$. If the height of block is H = 8.0 cm then height of the submerged part is ________ cm.

A soap bubble of surface tension 0.04 N/m is blown to a diameter of 7 cm. If (15000 - x) $$\mu J$$ of work is done in blowing it further to make its diameterl4 cm, then the value of x is_____.
$$\left(\pi=22/7\right)$$

Water drops fall from a tap on the floor, 5 m below, at regular intervals of time, the first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from ground, at the instant when the first drop strikes the ground is _____ m.
$$(g=10m/s^{2}$$

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

A ball of radius r and density $$\rho$$ dropped through a viscous liquid of density $$\sigma$$ and viscosity $$\eta$$ attains its terminal velocity at time t, given by $$t= A \rho^{a}r^{b}\eta^{c}\sigma^{d}$$, where A is a constant and a, b, c and d are integers. The value of $$\frac{b+c}{a+d}$$ is _________.

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)

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

A tube of length 1 m is filled completely with an ideal liquid of mass 2 M , 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 __________.

Two soap bubbles of radius 2 cm and 4 cm , respectively, are in contact with each other. The radius of curvature of the common surface, in cm , is ________ .

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

An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having surface tension $$0.095 J/m^{2}$$ and density $$10^{3}kg/m^{3}$$. The difference between pressure inside the bubble and atmospheric pressure is _____$$N/m^{2}.(\text{ take }g=10m/s^{2})$$

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

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

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:

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

A 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water ? (Given : density of water $$= 1000 kg m^{-3}$$)

A plane is in level flight at constant speed and each of its two wings has an area of $$40$$ m$$^2$$. If the speed of the air is $$180$$ km h$$^{-1}$$ over the lower wing surface and $$252$$ km h$$^{-1}$$ over the upper wing surface, the mass of the plane is ________kg. (Take air density to be $$1$$ kg m$$^{-3}$$ and $$g = 10$$ m s$$^{-2}$$)

Given below are two statements :

Statement (I) : Viscosity of gases is greater than that of liquids.

Statement (II) : Surface tension of a liquid decreases due to the presence of insoluble impurities. In the light of the above statements, choose the most appropriate answer from the options given below :

The reading of pressure metre attached with a closed pipe is $$4.5 \times 10^4$$ N m$$^{-2}$$. On opening the valve, water starts flowing and the reading of pressure metre falls to $$2.0 \times 10^4$$ N m$$^{-2}$$. The velocity of water is found to be $$\sqrt{V}$$ m s$$^{-1}$$. The value of $$V$$ is _____.

In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are $$70$$ m s$$^{-1}$$ and $$65$$ m s$$^{-1}$$ respectively. If the wing area is $$2$$ m$$^2$$, the lift of the wing is _______ N. (Given density of air $$= 1.2$$ kg m$$^{-3}$$)

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?

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:

Mercury is filled in a tube of radius $$2$$ cm up to a height of $$30$$ cm. The force exerted by mercury on the bottom of the tube is _____ N. (Given, atmospheric pressure $$= 10^5$$ Nm$$^{-2}$$, density of mercury $$= 1.36 \times 10^4$$ kg m$$^{-3}$$, $$g = 10$$ m s$$^{-2}$$, $$\pi = \frac{22}{7}$$)

A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of $$10$$ N is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is ______ N.

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 :

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

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 $$= 0.9$$)

Small water droplets of radius 0.01 mm are formed in the upper atmosphere and falling with a terminal velocity of 10 cm/s. Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be _____ cm/s.

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 :

A spherical ball of radius $$1 \times 10^{-4} \text{ m}$$ and density $$10^5 \text{ kg/m}^3$$ 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 $$9.8 \times 10^{-6} \text{ N s/m}^2$$)

The strain-stress plot for materials A, B, C and D is shown in the figure. Which material has the largest Young's modulus?

Two wires A and B made of different materials of lengths 6.0 cm and 5.4 cm, respectively and area of cross sections $$3.0\times 10^{-5}m^{2}\text{ and }4.5\times 10^{-5}m^{2}$$, respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of A to that of B is x : 3. The value of x is ___ .

The increase in pressure required to decrease the volume of a water sample by  $$0.2%$$  is  $$P \times10^5\,Nm^{-2}.$$ Bulk modulus of water is  $$2.15\times10^9\,Nm^{-2}.$$  The value of  $$P$$  is  $$\underline{\hspace{2cm}}.$$

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A:A sound wave has higher speed in solids than gases. Reason R: Gases have higher value of Bulk modulus than solids. In the light of the above statements, choose the correct answer from the options given below

The fractional compression $$(\frac{\Delta V}{V})$$ of water at the depth of 2.5 km below the sea level is ______%.Given, the Bulk modulus of water $$= 2\times 10^{9}Nm^{-2}$$, density of water $$= 10^{3}kgm^{-3}$$, acceleration due to gravity $$= g =10 m s^{-2}$$.

In an experiment with photoelectric effect, the stopping potential,

The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of $$7 \times 10^{6}Pa$$, would be ____ $$mm^{3}$$. (Given bulk modulus of copper $$= 1.4 \times 10^{11} Nm^{-2}$$)

One end of a metal wire is fixed to a ceiling and a load of 2 kg hangs from the other end. A similar wire is attached to the bottom of the load and another load of 1 kg hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be [Area of cross section of wire = $$0.005 \text{ cm}^2$$, $$Y = 2 \times 10^{11} \text{ N m}^{-2}$$ and $$g = 10 \text{ m s}^{-2}$$]

If average depth of an ocean is $$4000$$ m and the bulk modulus of water is $$2 \times 10^9 \text{ N m}^{-2}$$, then fractional compression $$\frac{\Delta V}{V}$$ of water at the bottom of ocean is $$\alpha \times 10^{-2}$$. The value of $$\alpha$$ is _______, (Given, $$g = 10 \text{ m s}^{-2}, \rho = 1000 \text{ kg m}^{-3}$$)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The property of body, by virtue of which it tends to regain its original shape when the external force is removed, is Elasticity.
Reason (R) : The restoring force depends upon the bonded inter atomic and inter molecular force of solid.
In the light of the above statements, choose the correct answer from the options given below :

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:

Two metallic wires $$P$$ and $$Q$$ have same volume and are made up of same material. If their area of cross sections are in the ratio $$4 : 1$$ and force $$F_1$$ is applied to $$P$$, an extension of $$\Delta l$$ is produced. The force which is required to produce same extension in $$Q$$ is $$F_2$$. The value of $$\frac{F_1}{F_2}$$ is ______.

Young's modulus 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 modulus will be:

Each of three blocks $$P$$, $$Q$$ and $$R$$ shown in figure has a mass of $$3 \text{ kg}$$. Each of the wire $$A$$ and $$B$$ has cross-sectional area $$0.005 \text{ cm}^2$$ and Young's modulus $$2 \times 10^{11} \text{ N m}^{-2}$$. Neglecting friction, the longitudinal strain on wire $$B$$ is $$\_\_\_\_ \times 10^{-4}$$. (Take $$g = 10 \text{ m s}^{-2}$$)

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by $$0.02\%$$ is _____ m. (Take density of sea water $$= 10^3 \text{ kg m}^{-3}$$, Bulk modulus of rubber $$= 9 \times 10^8 \text{ N m}^{-2}$$, and $$g = 10 \text{ m s}^{-2}$$)