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JEE • PHYSICS • MECHANICAL PROPERTIES OF SOLIDS

Mechanical properties of solids practice · Medium

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These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Showing 1-30 of 251 questions

1 Medium

1 of 251

Understanding +4 | -1

A wire is stretched under a force. If the wire suddenly snaps the temperature of the wire

View answer and explanation

Correct option: C

Increase

Option C (Increase) is correct because the work done in stretching the wire is converted into heat, increasing its temperature when the wire snaps.

2 Medium

2 of 251

Understanding +4 | -1

The increases in length is

l

of a wire of length

L

by the longitudinal stress. Then the stress is proportional to

View answer and explanation

Correct option: B

l/L

Option B (

l/L

) is correct because stress is proportional to strain, and strain is defined as change in length divided by original length.

3 Medium

3 of 251

Application +4 | -1

A steel wire of length

l

and cross sectional area

\mathrm{A}

is stretched by

1 \mathrm{~cm}

under a given load. When the same load is applied to another steel wire of double its length and half of its cross section area, the amount of stretching (extension) is

View answer and explanation

Correct option: C

4 \mathrm{~cm}

Option C (4 cm) is correct because the extension is directly proportional to the length and inversely proportional to the cross-sectional area.

4 Medium

4 of 251

Understanding +4 | -1

Assertion: From the relation

Y=\frac{F l}{A \Delta l},

we can say that, if length of a wire is doubled, its Young's modulus of elasticity will also becomes two times.

Reason: Modulus of elasticity is a material property.

View answer and explanation

Correct option: D

If Assertion is false but the Reason is true

Option D is correct because Young's modulus is a material property and does not depend on the dimensions of the wire, so the assertion is false, but the reason is true.

5 Medium

5 of 251

Application +4 | -1

A wire can be broken by applying a load of 200 N. The force required to break another wire of the same length and same material, but double in diameter, is

View answer and explanation

Correct option: D

800 N

Option D (800 N) is correct because the breaking force is proportional to the cross-sectional area, which is proportional to the square of the diameter.

6 Medium

6 of 251

Analyzing +4 | -1

Assertion(A): If radius of cylindrical wire is doubled, then this wire can bear four times stress.

Reason(R): By doubling the radius, area of cross-section will become four times.

View answer and explanation

Correct option: D

If Assertion is false but Reason is true.

Option D (If Assertion is false but Reason is true) is correct because stress is inversely proportional to the area, so doubling the radius reduces stress by a factor of four, and the area does become four times larger.

7 Medium

7 of 251

Application +4 | -1

A 10 kg load is suspended by a wire of cross section

0.1\,\,m{m^2}.

The stress produced in

N/{m^2}

View answer and explanation

Correct option: A

9.8 \times {10^8}

Option A (

9.8 \times {10^8}

) is correct because stress is defined as force per unit area, and in this case, the force is the weight of the load.

8 Medium

8 of 251

Application +4 | -1

A metallic cylinder has breaking stress of

{10^6}N/{m^2}

and density

2 \times {10^3}kg/{m^3}

. The maximum
possible height of the cylinder that can be hung from a rigid support is

View answer and explanation

Correct option: B

50 m

Option B (50 m) is correct because it is the maximum height calculated using the breaking stress, density, and gravity.

9 Medium

9 of 251

Application +4 | -1

A steel wire of length

3.2 \mathrm{~m}\left(Y_s=2.0 \times 10^{11} \mathrm{Nm}^{-2}\right)

and a copper wire of length

4.4 \mathrm{~m}\left(Y_c=1.1 \times 10^{11}\right.

\mathrm{Nm}^{-2}

), both of radius

1.4 \mathrm{~mm}

are connected end to end. When stretched by a load, the net elongation is found to be

1.4 \mathrm{~mm}

. The load applied, in Newton, will be: (Given

\pi=\frac{22}{7}

)

View answer and explanation

Correct option: D

154

Option D (154) is correct because it is the load calculated using the elongation formula considering both steel and copper wires connected in series.

10 Medium

10 of 251

Understanding +4 | -1

Choose the correct relationship between Poisson ratio

(\sigma)

, bulk modulus

(K)

and modulus of rigidity

(\eta)

of a given solid object

View answer and explanation

Correct option: C

\sigma=\frac{3 K-2 \eta}{6 K+2 \eta}

Option C is correct because the correct relationship between Poisson's ratio, bulk modulus, and modulus of rigidity is given by

\sigma=\frac{{3K-2\eta}}{{6K+2\eta}}

11 Medium

11 of 251

Application +4 | -1

Two wires of same length and of same material have diameters in the ratio

2: 3

. The elastic potential energy per unit volume for the wires, when stretched by the same force is

View answer and explanation

Correct option: C

\frac{81}{16}

Option D (

\frac{81}{16}

) is correct because the elastic potential energy per unit volume is inversely proportional to the fourth power of the radius (or diameter).

12 Medium

12 of 251

Application +4 | -1

A silica glass rod has a diameter of

1 \mathrm{~cm}

and is

10 \mathrm{~cm}

long. The ultimate strength of glass is

50 \times 10^6 \mathrm{~Nm}^{-2}

. Estimate the largest mass that can be hung from it without breaking it. Take

{g}=10 \mathrm{~N} \mathrm{~kg}^{-1}

View answer and explanation

Correct option: A

392.5 \mathrm{~kg}

Option A (

392.5 \text{ kg}

) is correct because it is calculated using the ultimate strength formula and the given parameters.

13 Medium

13 of 251

Analyzing +4 | -1

Given below are two statements : One is labelled as, Assertion (A) and the other is labelled as Reason (R)
Assertion (A) : The stretching of a spring is determined by the shear modulus of the material of the spring.
Reason (R) : A coil spring of copper has more tensile strength than a steel spring of same dimensions.
In the light of the above statements, choose the most, appropriate answer from the options given below

View answer and explanation

Correct option: D

(A) is true but (R) is false

Option D is correct. The stretching of a spring is determined by the shear modulus because it involves a change in shape, and copper has less tensile strength than steel.

14 Medium

14 of 251

Remembering +4 | -1

Substance which can be elastically stretched to large value of strain are called

View answer and explanation

Correct option: D

Elastomers

Option D (Elastomers) is correct because elastomers are polymers with viscoelasticity and very weak intermolecular forces, generally having low Young's modulus and high failure strain.

15 Medium

15 of 251

Understanding +4 | -1

A: Iron is more elastic than copper.
R: Under a given deforming force, Iron is deformed less than copper

View answer and explanation

Correct option: A

If both A

\&

R are true and the R is the correct explanation of the A

Option A (If both A & R are true and the R is the correct explanation of the A) is correct because iron's higher elasticity means it deforms less under the same force, which is why it's more elastic.

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16 Medium

16 of 251

Understanding +4 | -1

The longitudinal extension of any elastic material is very small. In order to have an appreciable change, the material must be in the form of

View answer and explanation

Correct option: C

long thin wire

Option C (long thin wire) is correct because the extension is directly proportional to the length and inversely proportional to the cross-sectional area.

17 Medium

17 of 251

Application +4 | -1

A metal bar of length

L

and area of cross-section

A

is clamped between two rigid supports. For the material of the rod, Young's modulus is

Y

and coefficient of linear expansion is

\alpha

. If the temperature of the rod is increased by

\Delta t^{\circ} \mathrm{C}

, the force exerted by the rod on the support is

View answer and explanation

Correct option: B

Y A \alpha \Delta t

Option B (

Y A \alpha \Delta t

) is correct because the force is calculated using Young's modulus, area, coefficient of linear expansion, and temperature change.

18 Medium

18 of 251

Understanding +4 | -1

{E_\mathrm{\theta }}\,\,\mathrm{and}\,\,{\mathrm{E}_\phi }

denote the isothermal and adiabatic elasticities respectively of a gas, then

\frac{{{E_\mathrm{\theta }}}}{{{\mathrm{E}_\phi }}}

View answer and explanation

Correct option: A

< 1

Option A (

< 1

) is correct because the ratio of isothermal to adiabatic elasticity is the inverse of the adiabatic index, which is always greater than 1.

19 Medium

19 of 251

Application +4 | -1

The elastic limit and ultimate strength for steel wire is

2.48 \times 10^8 \mathrm{~Pa}

and

4.89 \times 10^8 \mathrm{~Pa}

. A steel wire of length

10 \mathrm{~m}

and diameter of cross-section

2 \mathrm{~mm}

is given, then find maximum force that can be applied to ends of wire without breaking the wire

\left(\gamma_{\text {steel }}=2 \times 10^{11}\right)

View answer and explanation

Correct option: B

1535 \mathrm{~N}

Option B (

1535 \mathrm{~N}

) is correct because it is calculated using the breaking stress and the cross-sectional area of the wire.

20 Medium

20 of 251

Understanding +4 | -1

Choose the wrong statement.

View answer and explanation

Correct option: B

Gases are least compressible.

Option B is correct because gases are highly compressible due to the large spaces between their molecules, unlike solids which are much less compressible.

21 Medium

21 of 251

Analyzing +4 | -1

The relation between

Y, G

, and

B

is:

View answer and explanation

Correct option: B

\frac{9}{Y}=\frac{3}{G}+\frac{1}{B}

The correct relation between Young's modulus (Y), Shear modulus (G), and Bulk modulus (B) is given by Option B:

\frac{9}{Y}=\frac{3}{G}+\frac{1}{B}

22 Medium

22 of 251

Application +4 | -1

A cube is subjected to a uniform volume compression. It the side of the cube decreases by

2\,\,\%

, the bulk strain is

View answer and explanation

Correct option: D

0.06

Option D (0.06) is correct because the bulk strain is calculated as the change in volume divided by the original volume, which is approximately 3 times the percentage change in the side length.

23 Medium

23 of 251

Application +4 | -1

The increase in length of a wire on stretching is

0.025 \%

. If its Poisson's ratio is 0.4 , then the percentage decrease in diameter.

View answer and explanation

Correct option: A

0.01 \%

Option A (

0.01 \%

) is correct because it is calculated using Poisson's ratio and the percentage change in length.

24 Medium

24 of 251

Remembering +4 | -1

Stress is a _____ quantity.

View answer and explanation

Correct option: D

Tensor

Option D (Tensor) is correct because stress is defined as force per unit area, and it has different values depending on the direction, making it a tensor quantity.

25 Medium

25 of 251

Understanding +4 | -1

Which of the following statement(s) is/are correct?

I. Incompressible liquids have finite value of bulk modulus of elasticity.

II. Compressibility is inverse of bulk modulus of elasticity.

View answer and explanation

Correct option: B

Only II

Option B (Only II) is correct because incompressible liquids have an infinite bulk modulus, and compressibility is the inverse of the bulk modulus.

26 Medium

26 of 251

Application +4 | -1

A solid block of silver with density

10.5 \times {10^3}\,\,\mathrm{kg }{\mathrm{m}^{ - 3}}

is subjected to an external pressure of

{10^7}\,\mathrm{N}{\mathrm{m}^{ - 2}}

. If the bulk modulus of silver is

17 \times {10^{10}}\,\mathrm{N}{\mathrm{m}^{ - 2}}

, the change in density of silver ( in kg

{\mathrm{m}^{ - 3}})

View answer and explanation

Correct option: A

\mathrm{0}\mathrm{.61}

Option A (0.61) is correct because it is the change in density calculated using the bulk modulus formula and the given pressure.

27 Medium

27 of 251

Application +4 | -1

When a rubber cord is stretched, the change in volume with respect to change in its linear dimensions is negligible. The Poisson’s ratio for rubber is

View answer and explanation

Correct option: C

0.5

Option C (0.5) is correct because when the volume change is negligible, Poisson's ratio for rubber approaches 0.5.

28 Medium

28 of 251

Application +4 | -1

An elongation of 0.2% in a wire of cross section

{10^{ - 3}}\,{m^2}

causes a tension of 200 N.

Y

for the wire is

\left[ {\mathrm{in}\,\,N/{m^2}} \right]\,

View answer and explanation

Correct option: C

{10^8}

Option C (

{10^8}

) is correct because Young's modulus is calculated by dividing stress by strain.

29 Medium

29 of 251

Application +4 | -1

Forces of 100 N each are applied in opposite directions on the upper and lower faces of a cube of side

20\,cm

. The upper face is shifted parallel to itself by

0.25\,cm

. If the side of the cube were 10 cm, then the displacement would be

View answer and explanation

Correct option: B

0.5\,cm

Option B (

0.5\,cm

) is correct because the displacement is inversely proportional to the side of the cube, so halving the side doubles the displacement.

30 Medium

30 of 251

Remembering +4 | -1

Thermal stress, If developed in a solid on heating is given by

View answer and explanation

Correct option: A

y\frac{{\Delta l}}{l}

Option A (

y\frac{{\Delta l}}{l}

) is correct because thermal stress is related to Young's modulus and strain.

Revision notes and key takeaways

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Key Takeaways

✓ This set contains 251 single-correct-answer MCQs on MECHANICAL PROPERTIES OF SOLIDS.
✓ Try each question before opening its answer. Read the explanation where one is available.
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