JEE Main Previous Year Papers Questions With Solutions Physics Properties of Matter

JEE Main Previous Year Papers Questions With Solutions Physics Properties of Matter

Multiple Choice with ONE correct answer

1.A metal ball immersed in alcohol weighs W1 at 0°C and W₂ at 50° C . The co-efficient of cubical expansion of the metal is less than that of the alcohol. Assuming that the density of the metal is large compared to that of alcohol, it can be shown that   [1980-2 marks]
a )W1>W₂                   b)W1=W₂
c)W1<W₂                     d) All of these
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2.A vessel containing water is given a constant acce­leration ‘a’ towards the right along a straight horizontal path. Which of the following diagrams in fig. represent the surface of the liquid? [1981-2 marks]

Ans.(c) When a vessel containing water is given a constant acceleration a towards the right, a force acts on water towards right. As an action the water exerts a force on the wall of vessel towards right. As a reaction the wall pushes the water towards left. The slope of water is as shown in figure. P is a particle of water. F is the resultant of mg and ma. The surface of water should set it self at 90° to F.

3.The following four wires are made of the same material.Which of these will have the largest extension when the same tension is applied? [1981-2 marks]
a) length = 50 cm, diameter = 0.5 mm
b)length = 100 cm, diameter = 1 mm
c)length = 200 cm, diameter = 2 mm
d)length = 300 cm, diameter = 3 mm
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4.A U-tube of uniform cross-section (see fig) is partially filled with a liquid I. Another liquid II which does not mix with liquid I is poured into one side. It is found that the liquid levels of the two sides of the tube are the same, while the level of liquid I has risen by 2 cm. If the specific gravity of liquid I is 1.1, the specific gravity of liquid II must be      [1983-1 mark]

a) 1.12    b) 1.1    c) 1.05    d) 1.0
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5.A homogeneous solid cylinder of length L(L<H/2),cross-sectional area A/5 is immersed such that it floats with its axis vertical at the liquid-liquid interface with length L/4 in the denser liquid as shown in the figure. The lower density liquid is open to atmosphere having pressure P₀. Then density D of solid is given by  [1995]

a)5/4 d       b)4/5 d       c)4 d      d)d/5
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6.A large closed compartment containing gas is moving with some acceleration in horizontal directon. Neglect effect of gravity. Then the pressure in the compartment is [1999-2 marks]
a)same every where
b)lower in the front side
c)lower in the rear side
d) lower in the upper side
Ans.(b) Let the closed compartment containing gas move with horizontal acceleration a, along posi-tive side of x-axis. A pressure therefore acts on gas particles towards right. In the form of action, gas particles exert a pressure on the wall of the compartment towards right. In the form of reac-tion the wall exerts pressure on gas towards left. Hence the pressure is reduced on the front side.

7.A large open tank has two holes in the wall. One is a square hole of side L at a depth y from the top and the other is a circular hole of radius R at a depth 4y from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then, R is equal to: [2000-2 marks]

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10.A wooden block, with a coin placed on its top, floats in water as shown in figure. The distances l and h are shown here. After some time the coin falls into the water. Then   [2002-2 marks]

a)l decreases and h increases
b)l increases and h decreases
c)both l and h increase
d)both l and h decrease
Ans.(d) When the coin falls from the top of block into water, the block moves upwards because now the weight of floating body becomes less.Hence / decreases.When the coin is on the block, an equal weight of water is displaced. Let V2 be volume of water when the coin falls into water. An equal volume of water is displaced. Let V1 be volume of water which Is equal to volume of the coin/body itself.Density of water < Density of coin. Hence ft will decrease. Thus both l and h decrease.

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14.A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius R. End 2 has sub-hemispherical soap bubble as shown in figure. Just after opening the valve, [2008]

a)air from end 1 flows towards end 2. No change in the volume of the soap bubbles
b)air from end 1 flows towards end 2. Volume of the soap bubble at end 1 decreases
c)no change occurs
d)air from end 2 flows towards end 1. Volume of the soap bubble at end 1 increases
Ans.(b) We know that excess pressure in a soap bubble is inversely proportional to its radius. The soap bubble at end 1 has small radius as compared to the soap bubble at end 2 (given). Therefore excess pressure at 1 is more. As the valve is opened, air flows from end 1 to end 2 and the volume of soap bubble at end 1 decreases.

Multiple Choice with ONE or More Than ONE correct answers
15.A body floats in a liquid contained in a beaker. The whole system as shown in figure falls freely under gravity. The upthrust on the body is [1982-3 marks]

a)zero
b)equal to the weight of the liquid displaced
c)equal to the weight of the body in air
d)equal to the weight of the immersed portion of the body
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17.The spring balance A reads 2 kg with a block m suspended from it. A balance B reads 5 kg when a beaker with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid in the beaker as shown in the figure. In this situation [1985-2 marks]

a)the balance A will read more than 2 kg
b)the balance B will read more than 5 kg
c)the balance A will read less than 2 kg and B will read more than 5 kg
d)the balance A and B will read 2 kg and 5 kg respectively.
Ans.(b), (c) When the hanging mass is inside the liq¬uid, the liquid will apply an upthrust on the mass. Hence the balance A will read less than 2 kg. Infact m loses a weight when dipped in a liquid. An upthrust acts on block m.By reaction, an equal force will be exerted on the liquid contained in beaker in the downward direction.Hence g will read more than 5 kg.Hence (b) and (c) both are correct.
Infact (b) is contained in (c). So it is adequate to say that (c) holds good.

18.A vessel contains oil (density = 0.8 g/cm³) over mercury (density = 13.6 g I cm³ ). A homogeneous sphere floats with half its volume immersed in mercury and the other half in oil. The density of the material of the sphere in g/cm³ [1988-2 marks]
a)3        b) 6.4        c) 7.2         d) 12.8
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a)2:3 b)1:1 c)3:2 d)4:9
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20.Water from a tap emerges vertically downwards with an initial speed of 1.0 ms^-1. The cross ­sectional area of the tap is 10^-4 m². Assume that the pressure is constant throughout the stream of water, and that the flow is steady. The cross­sectional area of the stream 0.15 m below the tap is      [1998-2 marks]
a) 5.0 x 10-⁴ m² b) 1.0 x 10-⁵ m²
c) 5.0 x 10-⁵ m²  d)2.0 x 10-⁵ m²
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22.Two solid spheres A and B of equal volumes but of different densities d_A and d_B are connected by a string. They are fully immersed in a fluid of density dE. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if


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Assertion & Reasoning type
Instructions :The following question contains statement-I (assertion) and statement -2 (reason) Of these statements, mark correct choice if
a)Statements-1 and 2 are true and statement-2 is a correct explanation for statement-1
b)Statements-1 and 2 are true and statement-2 is not a correct explanation for statement-1
c)Statement-1 is true, statement-2 is flase
d)Statement-1 is false, statement-2 is true.

23.Statement – l:The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down. 
Statement – 2:In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.     [2008]
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Comprehension based  questions
Read the passage given below and answer the following questions
A cylindrical tank has a hole of diameter 2r in its bottom. The hole is covered by a wooden cylindrical block of diameter 4r, height h and density p/ 3
Situation – 1: Initially, the tank is filled with water of density p to a height such that the height of water above the top of the block is /z, (measured from the top of the block).
Situation – 2:The water is removed from die tank to a height K (measured from the bottom of the block), as shown in the figure. The height ^ is smaller than h (heigh of the block) and thus the block is exposed to the atmosphere.

24.Find the minimum value of height h1 (in situation 1) for which the block just starts to move up ?[2006-5 marks]
a)2h/3   b)5h/4     c)5h/3    d)5h/2
Ans.(a)

25.Find the height of the water level (in situation 2), for which the block remains in its original position without the application of any external force [2006-5 marks]
a) h/3      b)4h/9   c)2h/3  d)h
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26.In situation 2, if is further decreased, then [2006-5 marks]
a)cylinder will not move up and remains at its original position
b)for  h2 =h/3 , cylinder again starts moving up
c)for h2 =h/4, cylinder again starts moving up
d)for h2 =h/5, cylinder again starts moving up
Ans.(a) (iii) When the height h2 of water level is further decreased, in situation 2, then the upward force acting on the wooden block decreases. The total downward force remains the same. The normal reaction by the tank wall on the wooden block adjuist the difference. The block will not move up and remains at its original position.

Read the passage given below and answer the following questions
A fixed thermally conducting cylinder has a radius R and height Lq . The cylinder is open at its bottom and has a small hole at its top. A piston of mass M is held at a distance L from the top surface, as shown in the figure. The atmospheric pressure is P₀

27.The piston is now pulled out slowly and held at a distance 2L from the top. The pressure in the cylinder between its top and the piston will then be   [2007-4 marks]

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28.While the piston is at a distance 2L from the top, the hole at the top is sealed. The piston is then released, to a position where it can stay in equilibrium. In this condition, the distance of the piston from the top is [2007-4 marks]

Ans.(d) Let the pressure of the trapped air be P. Draw the forces on the piston.
For the equilibrium of the piston,

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30.As the bubble moves upwards, besides the buoyancy force the following forces are acting on it.          [2008]
a)Only the force of gravity
b)The force due to gravity and the force due to the pressure of the liquid
c)The force due to gravity, the force due to the pressure of the liquid, and the force due to viscosity of the liquid
d)The force due to gravity and the force due to viscosity of the liquid.
Ans.(d) The buoyancy force is the force on the bubble due to the pressure of the liquid. In addition to this force, two more forces act on the bubble, the weight of the gas in the bubble and the viscous force on the bubble.

31.When the gas bubble is at a height y from the bottom, its temperature is      [2008]

Ans.(b) The bubble does not exchange any heat with the liquid. So the gas in the bubble undergoes an adiabatic process.

32.The buoyancy force acting on the gas bubble is (assume R is the universal gas constant) [2008]

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Read the passage given below and answer the following questions
When liquid medicine of density p is to put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at the opening is spherical because that requires a minimum increase in it surface energy. To determine the size, we calculate the net vertical force due to the surface tension T when the radius of the drop is R. When this force becomes smaller than the weight of the drop, the drop gets detached from file dropper.

33.If the radius of the opening of the dropper is r, the vertical force due to the surface tension on the drop of radius R (assuming r<<R) is

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35.After the drop detaches, its surface energy is 

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Subjective / Numerical integer type
36.A column of mercury of length 10 cm is contained in the middle of a horizontal tube of length l m which is closed at both the ends. The two equal lengths contain air at standard atmospheric pressure of 0.76 m of mercury. The tube is now turned to vertical position. By what distance will the column of mercury be displaced ?          [1978]
Ans.Let A cm2 be the area of cross-section of the tube. When the tube is in the horizontal position, as shown in the figure (a), the length of the air column on the left hand (region I) and right hand side region II of the mercury column is 45 cm each, the total length of the tube being 100 cm with the mercury column length 10 cm in the middle. r The pressure of air in each half is P=76 cm of mercury and the volume of air in each half is ‘ V = 45A cm3.
When the tube is turned to vertical position, as shown in figure (b), the mercury column is dis-placed downwards. Let xcm be the length of air column I when the mercury column attains equi-librium. Volume of column I is V1=A x cm3 and let Pj cm of Hg be the pressure of air in column I. The length of column II is (90 – x) cm and its volume is V2=(90 – X) A cm3. Let the pressure of air in column II be P2 cm of Hg.

37.A boat floating in a water tank is carrying a number of large stones. If the stones are unloaded into water, what will happen to the water level? [1979]
Ans.The reading of the level of the water will lower down. Let the weight of the boat = Wg Weight of the stones = w g

38.Two identical cylindrical vessels with their bases at the same level each contain a liquid of density The height of the liquid in one vessel is and in other vessel is . The area of either base is A. What is the work done by gravity in equalizing the levels when the two vessels are connected.[1981-4 marks]
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Ans.Consider the equilibrium of the plank hinged at O which is at one end at the bottom of tank. Three forces act upon it :
(i)Weight of plank. It acts downwards at the centre of the plank. Let it be W.
(ii)Upthrust of water. It acts at the centre of submerged portion of plank. Let it be F.
(iii)Force from the hinge at O.
Take moment of the forces about O. Moment of hinge force will be zero as its distance from O is zero. It infact it passes through O.Moment of weight W= Moment of upthrust F

40.A thin tube of uniform cross-section is sealed at both ends. It lies horizontally, the middle 5 cm containing mercury and the two equal ends containing air at the same pressure P. When the tube is held at an angle of 60° with the vertical direction, the length of the air column above and below the mercury column are 46 cm and 44.5 cm respectively. Calculate the pressure P in centimetre of mercury. (The temperture of the system is kept at 30° C).    [1986-6 marks]
Ans.Initially the tube is horizontal. Then it is held at 60° with vertical. The temperture remains constant at 30°C.Boyle’s law can be applied to horizontal AB and inclined AB portions, in the two positions.

41.A ball of density d is dropped on to a horizontal solid surface. It bounces elastically from the surface and returns to its original position in a time t₁. Next, the ball is released and it falls through the same height before striking the surface of a liquid of density of d_L
a)If d<d_L, obtain an expression (in terms of d,t1 and d_L) for the time t₂ the ball takes to come back to the position from which it was released.
b)Is the motion of the ball simple harmonic?
c)If d = d_L, how does the speed of the ball depend on its depth inside the liquid ? Neglect all frictional and other dissipative forces. Assume the depth of the liquid to be large.   [1992-8 marks]
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The velocity remain constant. It does not change with depth inside the liquid.

42.A container of large uniform cross-sectional area A resting on a horizontal surface, holds two immiscible, non—viscous & incompressible liquids of densities d & 2d , each of height H/2 as shown in figure . The lower density liquid is open to the atmosphere having pressure P_o.



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44.A large open container of negligible mass and uniform cross-sectional area A has a small hole of cross-sectional area A/100 in its side wall near the ‘ bottom. The container is kept on a smooth horizontal floor and contains a liquid of density p and mass m₀. Assuming that the liquid starts flowing out horizontally through the hole at t=0, Calculate
i)the acceleration of the container, and
ii)its velocity when 75% of the liquid has drained out.   [1977-5 marks]
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47.A uniform solid cylinder of density 0.8 gm/cm³ floats in equilibrium in a combination of two non mixing liquids A and B with its axis vertical. The densities of the liquids A and B are 0.7 gm/cm³respectively. The height of liquid A is h_A = 1.2 cm. The length of the part of the cylinder immersed in liquid B is h_B = 0.8 cm.  [2002-5 marks]

a)Find the total force exerted by liquid A on the cylinder.
b)Find h, the length of the part of the cylinder in air.
c)The cylinder is depressed in such a way that its top surface is just below the upper surface of liquid A and is then released. Find the acceleration of the cylinder immediately after it is released.
Ans.(a) Total force exerted by liquid A on cylinder : The liquid + is exerting force on the cylinder sym-metrically from all the sides.

48.A bubble having surface tension T and R radius is formed on a _v ring of radius b(b<<R). Air is blown inside the tube with velocity vas shown. The air molecule collides perpendicularly with the wall of the bubble and stops. Calculate the radius at which the bubble separates from the ring.

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52.A small sphere falls from rest in a viscous liquid. Due to friction, The medium gets heated. How does the rate of heating depend on radius of body when it attains terminal velocity ? [2004-2 marks]
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54.Two soap bubbles A and B are kept in a closed chamber where the air is maintained at pressure 8 N/m². The radii of bubbles A and B are 2 cm and 4 cm, respectively. Surface tension of the soap-water used to make bubbles is 0.04 N/m. Find the ratio n_B/n_A, where n_A and n_B are the number of moles of air in bubbles A and B, respectively. [Neglect the effect of gravity.]     (2009)
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55.A cylindrical vessel of height 500 mm has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it upto height H. Now the top is completely sealed with a cap and the orifice at the bottom is opened. Some water comes out from the orifice and the water level in the vessel becomes steady with height of water column being 200 mm. Find the fall in height (in mm) of water level due to opening of the orifice. 
[Take atmospheric pressure = 1.0 x 10⁵ N/m², density of water = 1000 kg/m³ and g = 10 m/s². Neglect any effect of surface tension][2009]
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56.Steel wire of length ‘L’ at 40°C is suspended from the ceillling and then a mass ‘m’ is hung from its free end. The wire is cooled down form 40°C to 30°C to regain its original length ‘L’ .The coefficient of liner thermal expansion of the steel is 10^-5/°C, Young’s modulus of steel is 10¹¹ N/m² and radius of the wire is 1 mm. Assume that L>> diameter of the wire. Then the value of ‘m’ in kg is nearly  [2011]
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True/False Type
57.A man is sitting in a boat which is floating in a pond. If the man drinks some water from the pond, the level of the water in the pond decreases. [1980]
Ans.False The level of water will remain the same because when the man drinks some water froih the pond, , the liquid displaced become more so as to main¬tain the original level.

58.A barometer made of a very narrow tube (see fig) is placed at normal temperature and pressure. The coefficient of volume expansion of mercury is 0.00018 per°C and that of the tube is negligible.The temperature of mercury in the barometer is now raised by 1 °C > but The temperature of the atomosphere  does  not change. Then the mercury height in the tube remains unchanged.  [1983-2 marks]

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59.Water in a closed tube (see fig) is heated with one arm vertically placed above a lamp. Water will  begin to circulate along the tube in counter clockwise direction. [1983-2 marks]

Ans.False When the tube is heated at A, the density of water will decrease and the water will rise up to flow towards B. Water will begin to circulate along the tube in clock wise direction.

60.A block of ice with a lead shot embedded in it is floating on water contained in a vessel. The temperature of the system is maintained at 0°C as the ice melts. When the ice melts completely the level of water in the vessel rises. [1986-3 marks]
Ans.False The level of water, in the vessel, falls. Melting of ice-block merely by it self, does not cause any change in level of water on which it floats.
Lead shot, embedded in ice block, floats on water. The change in level of water will be due to this lead shot which initially floats but finally sinks into water when ice-block melts, v Mass of floating lead-shot = Mass of water dis¬placed = M

61.A uniform glass tube of internal radius (1) has a valve separating the identical ends. Imitialy the value is in a tight in closed positional. End 2 has a hemisphatical soap babble of radius r and end 2 has a small hemispherical soap bubble as in fig. Just after.changing the value [2008]
a)air from ends 1 floor towards end 2 no change in the volume of soap bubble
b)air from end 1 hows towards end 2 volume of the soap bubble at end 2 decrease
c)No changes over
d)air from end 2 floor towards end 1 volume of the soap bubble at end 1 decreases.
Ans.(b)

62.A 0.1 kg mass is suspended from a wire of negli­gible mass . The length of the wire is 1 m and its cross-sectional area is 4.9 x lO^-7 m². If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad S^-1. If the Young’s modulus of the material of the wire is n x lO⁹ Nm^-2, the value of n is

Fill in the blanks
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63.A wire of length L and cross-sectional area A is made of a material of Young’s modulus Y. If the wire is stretched by an amount x, the work done is………………………………………….  [1987-2 marks]
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66.A horizontal pipe line carries water in a streamline flow. At a point along the pipe where the cross-sectional area is 10 cm² , the water velocity is 1 ms^-1 & the pressure is 2000 Pa. The pressure of water at another point where the cross sectional area is 5 cm², is…………… pa [ Density of water = 10³ kg. m^-3] [1994-2 marks]
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