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NEET • PHYSICS • MECHANICAL PROPERTIES OF SOLIDS

Mechanical properties of solids practice · Hard

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1 Hard

1 of 11

Application +4 | -1

A stress of

10^6 \mathrm{Nm}^{-2}

is required for breaking a material. If the density of the material is

3 \times 10^3 \mathrm{kgm}^{-3}

, then what should be the length of the wire made of this material, so that it breaks under its own weight?

View answer and explanation

Correct option: B

33.3 \mathrm{~m}

Option B (

33.3 \mathrm{~m}

) is correct because the length is calculated by equating the stress due to the wire's weight to the breaking stress of the material.

2 Hard

2 of 11

Application +4 | -1

A circular tube of mean radius

8 \mathrm{~cm}

and thickness

0.04 \mathrm{~cm}

is melted up and recast into a solid rod of the same length. The ratio of the torsional rigidities of the circular tube and the solid rod is

View answer and explanation

Correct option: A

\frac{(8.02)^4-(7.98)^4}{(0.8)^4}

Option A (

\frac{{(8.02)^4-(7.98)^4}}{{(0.8)^4}}

) is correct because the torsional rigidity is proportional to the polar moment of inertia, which depends on the radius to the fourth power for a tube and a solid rod.

3 Hard

3 of 11

Application +4 | -1

The maximum stress that can be applied to the material of a wire used to suspend an elevator is

1.3 \times 10^8 \mathrm{~Nm}^{-2}

. If the mass of the elevator is

900 \mathrm{~kg}

and it moves up with an acceleration of

2.2 \mathrm{~ms}^{-2}

, what is the minimum diameter of the wire?

View answer and explanation

Correct option: A

1.0284 \times 10^{-{2}} \mathrm{~m}

Option A (

1.0284 \times 10^{-{2}} \mathrm{~m}

) is correct because it is the minimum diameter of the wire calculated based on the maximum stress, mass, and acceleration of the elevator.

4 Hard

4 of 11

Application +4 | -1

A cable is replaced by another one of the same length and material but of twice the diameter. The maximum load that the new wire can support without exceeding the elastic limit, as compared to the load that the original wire could support, is

View answer and explanation

Correct option: C

four times

Option C (four times) is correct because the maximum load a wire can support is proportional to its cross-sectional area, which is proportional to the square of the diameter.

5 Hard

5 of 11

Understanding +4 | -1

If Poisson's ratio

\sigma

for a material is

-\frac{1}{2}

, then the material is

View answer and explanation

Correct option: B

incompressible

Option B is correct. A Poisson's ratio of -1/2 indicates that the material's volume remains constant under deformation, which is the definition of incompressibility.

6 Hard

6 of 11

Application +4 | -1

If Youngs moduls of a material is

10^8 \mathrm{~N} / \mathrm{m}^2

and coefficient of Rigidity is

3 \times 10^8 \mathrm{~N} / \mathrm{m}^2

then its bulk modulus will be-

View answer and explanation

Correct option: A

12.5 \times 10^6 \mathrm{~N} / \mathrm{m}^2

Option A (

12.5 \times 10^6 \mathrm{~N} / \mathrm{m}^2

) is correct because it is the calculated bulk modulus using the given Young's modulus and coefficient of rigidity.

7 Hard

7 of 11

Application +4 | -1

A steel wire of length 2 m and Young's modulus

2.0 \times 10^{11} \mathrm{Nm}^{-2}

is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and

10^{-3}

respectively, then the elastic potential energy density of the wire is _____

\times 10^5

(in SI units)

View answer and explanation

Correct option: A

Option A (25) is correct because the elastic potential energy density is calculated using the formula involving Young's modulus and transverse strain.

8 Hard

8 of 11

Application +4 | -1

If compressibility of a material is

4 \times 10^{-5}

per atm, pressure is

100 \mathrm{~atm}

and volume is

100 \mathrm{~cm}^3

, then find the value of

\Delta V

View answer and explanation

Correct option: A

0.4 \mathrm{~cm}^3

Option A (

0.4 \mathrm{~cm}^3

) is correct because it is the correct change in volume calculated using the compressibility formula.

9 Hard

9 of 11

Application +4 | -1

The density of a metal at normal pressure is

\rho

. Its density when it is subjected to an excess pressure

p

\rho^{\prime}

. If

B

is the bulk modulus of the metal, then the ratio

\rho^{\prime} / \rho

View answer and explanation

Correct option: D

\frac{1}{(1-p / B)}

Option D (

\frac{{1}}{{(1-p / B)}}

) is correct because it relates the change in density to the applied pressure and the bulk modulus.

10 Hard

10 of 11

Application +4 | -1

A rigid bar of mass

M

is supported symmetrically by three wires each of length

L

. Those at each end are of copper and the middle one is of iron. The ratio of their diameters, if each is to have the same tension, is equal to

View answer and explanation

Correct option: B

\sqrt{\frac{Y_{\text {iron }}}{Y_{\text {copper }}}}

Option B (

\sqrt{\frac{Y_{\text {iron }}}{Y_{\text {copper }}}}

) is correct because the ratio of diameters is related to the square root of the ratio of Young's moduli to maintain the same tension in each wire.

11 Hard

11 of 11

Application +4 | -1

A copper wire

\left(Y=10^{11} \mathrm{Nm}^{-2}\right)

of length

8 \mathrm{~m}

and a steel wire

\left(Y=2 \times 10^{11} \mathrm{Nm}^{-2}\right)

of length

4 \mathrm{~m}

, each of

0.5 \mathrm{~cm}^2

cross-section are fastened end-to-end and stretched with a tension of

500 \mathrm{~N}

. Choose the correct statement.

View answer and explanation

Correct option: D

All of the above

Option D (All of the above) is correct because the elongation in each wire, the relationship between them, and the total elongation are all accurately calculated and consistent with the given information.

Revision notes and key takeaways

Review MECHANICAL PROPERTIES OF SOLIDS in your textbook or class notes, then use this set to check your understanding.

Key Takeaways

✓ This set contains 11 single-correct-answer MCQs on MECHANICAL PROPERTIES OF SOLIDS.
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