jee mains questions on mechanical properties of solids

jee mains questions on mechanical properties of solids

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Today, we are going to cover the MOST IMPORTANT QUESTION on jee mains questions on mechanical properties of solids for exams like CBSE board, NEET, JEE MAIN & JEE ADVANCE.

First try to solve the question on your own in the allotted time as shown in table. Then check the answers.

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is at the end of the session.

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Let's crack it.

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Section	no of questions	Alloted Time	Type	Question level
Type 1	10	45 min	Mcq	Moderate
Type 2	5	--	Integer	Moderate
Type 3	5	--	Mcq	Tough

Quick Recap

Matter

Any substance which has mass and occupies space.

States of matter

Solid
Liquid
Gas

Pascal law 

If the pressure at some point in a fluid is changed, there will be an equal change in pressure at any other point

Buoyant Force

It is the upward force acting on the body immersed in a liquid. It is equal to the weight of the liquid displaced by the immersed part of the body.

Relative density 

 Ratio of density of substance to the density of water at 4°C.

Upthrust

 The upward force on the object immersed in fluids

Archimedes Principle 

When a body is immersed in liquid at rest, it appears lighter, this apparent loss of weight is equal to the weight of liquid displaced by the immersed part of the body
Apparent weight =actual weight- upthrust

Intermolecular forces 

 Cohesive force
Intermolecular force of attraction acting between the molecules of same substance

Adhesive force
Intermolecular force of attraction acting between the molecules of different ubstance

Surface tension

 T=F/l
Unit is N/m

Surface energy 

S.E.= T×δA

Jerlins equation

h=2T cosθ/rdg

Equation of continuity 

When a liquid is in streamline motion in a tube of non uniform cross-sectional area, then at each point on the path of liquid, the product of the area of cross-sectional area and the velocity of liquid is constant
a₁v₁= a₂ v₂

Bernoulli theorem

p +1/2dv²+ dgh= constant

Viscosity

F= -ηAdv/dt

Stokes Law

 F=6πηrv

 Terminal speed

v= 2r²(d-σ)g/9η




Let's begin

TIMER:

45min

Type 1 MCQ

1. A small pellet of mercury is introduced into a capillary tube as shown in figure. If in position A, its length is 1.00 cm while at B it is 1.01 cm, then the variation of radius of the capillary 

a.2.01%
b.0.5%
c.1.0%
d.4%

2. A solid sphere of radius R made of material of bulk modulus K is surrounded by liquid cylinder container. A massless piston of area A floats on the surface of liquid when the mass m is placed on the piston to compress the liquid the fractional change in radius of sphere δR/R is

a. Mg/3AK
b. Mg/AK
c.2Ak/Mg
d.2Mg/AK

 3. A block of wood floats in water with 4/3 part under water. If it floats in another liquid with 9/10 part under it, then the relative density of this liquid be

a.0.79
b.1.0
c.0.89
d.0.59

4. A horizontal pipeline carries water in streamline flow. At a point along the pipe where the cross section area is 10cm², the water velocity is 1ms^-1 and pressure is 2000Pa. Pressure of water at another point where cross sectional area is 5cm²is
Density of water is 1000kg.m^-3.

a.200
b.100
c.700
d 500

5. A small steel ball is dropped in a tall wide glass cylinder containing a viscous liquid. The change in velocity v with depth h is most appropriately represented by the curve (as shown in the figure) labelled 

a.A
b.B
c.C
d D

6. A homogeneous solid cylinder of length L, cross sectional area A/5 is immersed such that it float with its axis vertical at liquid liquid interface with length L/4 in denser liquid as shown in figure. The lower density liquid is open to atmosphere having pressure P_o. Then density D of the solid is given by

a.5d/4
b.4d/5
c.4d
d d/5

7. Mosquitoes can lay eggs on the surface of water. But when oil sprinkled on the surface of water, mosquitoes cannot lay eggs because 

a.Surface tension of water is increased
b.viscosity of water increases
c.surface tension of water is increased
d water-oil mixture acts as a mosquito repellant

8. A large tank has two holes in the wall. One is the square hole of side L at a depth y from the top and another is a circular hole of radius R at 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 same. Then R is equal to

a.L/√2π
b.2πL
c.L
d L/2π

9. If two soap bubbles of different radii are contacted by tube

a.air flows from smaller bubble to bigger
b.air flows from bigger bubble to smaller till the sizes interchanged
c.air flows from bigger bubble to smaller bubble till the sizes become equal
d there is no flow of air

10. Small drops of a liquid are spherical in shape because 

a.the earth attracts all the particles of the drop equally
b.the surface energy is minimum for the spherical shape
c.the surface energy is maximum for the spherical shape
d for a given volume the surface area if a sphere is maximum

Type 2        NUMERICAL TYPE

1. A weather forecasting meteorological balloon of volume 10m³ contains hydrogen of density 0.09 kg/m ³ and its fabric mass is 6.5kg. If it is floating in air density 1.25 kg/m³, then the mass of the equipment, it carries would be

2. A U-tube of uniform cross section is partially filled with a liquid l. Another liquid ll which is does not mix with liquid l is poured into one side. It is found that liquid level of two side of tube are the same, while the liquid of level l has risen by 2cm. If the specific gravity of the liquid l is 1.1., the specific gravity of liquid ll must be 

3. A 20cm long capillary tube is dipped in water. The water rises upto 8cm. If the entire arrangement is put into a freely falling elevator the length of water columnin capillary tube will be (in cm)

4. If the terminal speed of a sphere of gold (density=19.5 kg/m³ is 0.2m/s in viscous liquid (density= 1.5 kg/m³), find the terminal speed of a sphere (density =10.5 kg/m³) of the same size in same liquid (m/s)

5. Two identical charged spheres are suspended by strings of equal length. The strings make an angle 30° each other. When suspended in liquid of density 0.8 g/cm², the angle remains the same. If the density of the material of the sphere is 1.6g/cm³, the dielectric constant of liquid is

Type 3    JEE ADVANCE 

1. A glass capillary tube is of the shape of truncated cone with special angle α so that its two ends have cross sections of different radii when dipped in water vertically water rises in it to a height h, where the radius of cross section is b. If the surface tension of water is S, its density is ρ and its contact angle with glass is θ the value of h will be ( g is acceleration due to gravity)   

a.2Scos(θ-α)/bρg
b. 2Scos(θ+α)/bρg
c. 2Scos(θ-α/2)/bρg
d. 2Scos(θ+α/2)/bρg

2. A sphere Pand Q of equal tension of densities ρ₁ and ρ₂ respectively, the sphere are contracted by massless string placed in liquid L₁ and L₂ of densities σ₁ and σ₂ and viscosity η₁ and η₂, respectively. They float in equilibrium with sphere P in L₁ and Q in L₂ and string being taut (see figure). If sphere P alone in L₂ has terminal velocity V_P and Q alone in L₁ has terminal velocity V_Q, then

a. |V_P/V_Q|=η₁/η₂
b. |V_P/V_Q| = η₁/η₁
c. V_P.V_Q>0
d. V_P.V_Q<0

3. A uniform solid cylinder of density 0.8 g/cm³ floats in liquid in a combination of two non mixing liquid A and B with its vertical axis.
The density of liquid A and B are 0.7g/cm ³ and 1.2g/cm³ respectively. The height of liquid A is h_A=1.2cm and the length of part of cylinder immersed in liquid B is h_B =0.8cm
Find the total force exerted by liquid A on the cylinder

a.zero
b.non-zero
c.can't be predicted
d.undefined

4. As shown in the figure is a container whose top and bottom diameter are D and d respectively. At the bottom of the container, there is capillary tube of outer radius b and inner radius a.
The volume flow rate in capillary is Q. If the capillary is removed the liquid comes out with velocity v_o. The density of the liquid is given as ρ. The coefficient of viscosity η is given by kρv²(1- d⁴/D⁴)a⁴. Calculate k.

a.π/Ql
b.π/16Ql
c.1/Ql
d.π/8Ql

5. A U-tube rotated about one of it's limbs with angular velocity ω Find the difference in height h of the liquid (density ρ ) level, where diameter of the tube d<<l. 

a.ω²L²/2g
b.ω²L²/g
c.7ω²L²/g
d.5ω²L²/2g

Download the detailed answer pdf of the most important questions from Chapter
jee mains questions on mechanical properties of solids.

Unit and measurements  most important  questions	click here
Kinamatic most important questions	click here
Law of motion most important questions	click here
Work, energy and power most important questions	click here
Nit cutoff	click here
Iiit cutoff	click here

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mind-blowing facts about the universe

1. Most vacuumed place In our universe is spaces between the galaxies.

 2. There are 11 parallel dimensions
 (1) . Length
 (2). Width
 (3). Height
 (4). Time
 (5). Gravity/Energy
 (6)-(10). These are theoretically existing due to the string theory concept.
 (11). This is M-Theory

 3. Scientists predicted that there must be a multi-universe which follow there own rules of physics. And which may or may not be identical to our universe.

 4. Quasars are the brightest interstitial bodies in our universe

 5. The diameter of our universe is more than 98 billion light-years.

 6. Closest person you see around you is 1 by billionth second older, which means everything around you is already happened at there own specific time and Conditions.
 The reason for it is because light need to time to travel from one place to another.
 Similarly as light from the sun takes 8 minutes to reach earth.

 7. Light year is distance.

 8. The visible portion of the black holes is not the front one. It is because bend the light in such a way that emerges light show us it's backside which makes it more difficult to understand it.

 9. In the quantum world has it's own physics rules which are entirely different and beyond our imagination.

 10. Venus is the hottest planet in our solar system, not Mercury

 11. Some theories revealed that there is a planet between Jupiter and Mars which burst and turned into an asteroid belt.

 12. Every year moon is moving 3 cm away from earth.

 13. The first person on landed moon was Neil Armstrong. Can you guess the second one?

 14. Tides in oceans are because of the gravitational pull of the moon towards itself.

 15. Sun is not yellow is white.
 And Everything in outer space is black and white even earth.

 16. In our universe, nothing is two dimensional.

 17. We can't see black holes. They are visible because of the diameter around them.

 18. Mars still the only planet where life possible.

19. Red giant a storm on Jupiter which is as big as three times of earth and was there from the last 1000 thousand years.

20. There are 1000 thousands of other interstitial bodies revolving around the sun other than our 9 planets.

21. Andromeda is the closest galaxy and it may collide to our Milky way galaxy.
This collision looks so beautiful but it doesn't affect much to our solar system.

22. Our galaxy named Milky way because it has thousands of stars which makes our galaxy looks like milk.

23. Our universe was 13.8 billion light-years older and was named the big bang.

24. Some theories revealed that our earth also has a ring-like Saturn but due to gravitational pull it converted into moon.

25. Most of Jupiter is gas.

26. In 2006, NASA found "space roar" it's a sound that is six times louder than anything that anyone was expecting.
space roar isn't a sound, it's radio waves.


27. More than 80 percent of our universe contains Dark Matter and Dark energy.
And we don't even know what are they?

28. Earth is rotating on its axis with a speed of 1,600 km per hour, Earth is revolving around sun with Average speed 30 kilometers per second. Our solar system revolving main our Milky way galaxy with speed of 828,000 km/h. Now you may sum up all speeds.

29. How is it possible one change from non-living to living creatures?

30. The biggest mystery " Meaning of life?"


31. The big picture

Sounds of Saturn: Hear Radio Emissions of the Planet

     

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