The relationship between Young’s modulus $Y$, Bulk modulus ${\rm{K}}$ and modulus of rigidity $\eta $ is

$Y = \frac{{9\,\eta K}}{{3 + K}}$

$Y = \frac{{3\,\eta K}}{{9\eta + K}}$

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NEET • PHYSICS • MECHANICAL PROPERTIES OF SOLIDS

Mechanical properties of solids practice · Medium

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Showing 1-30 of 123 questions

1 Medium

1 of 123

Remembering +4 | -1

In magnitude hydraulic stress is equal to:

View answer and explanation

Correct option: B

Hydraulic pressure

Option B (Hydraulic pressure) is correct because hydraulic stress is defined as the applied hydraulic pressure.

2 Medium

2 of 123

Remembering +4 | -1

Stress to strain ratio is equivalent to

View answer and explanation

Correct option: A

modulus of elasticity

Option A (modulus of elasticity) is correct because the modulus of elasticity is defined as the ratio of stress to strain.

3 Medium

3 of 123

Application +4 | -1

2\,\,m

long rod of radius

1\,\,cm

which is fixed from one end is given a twist of

0.8

radians. The shear strain developed will be

View answer and explanation

Correct option: B

0.004

Option B (0.004) is correct because the shear strain is calculated as the ratio of the arc length at the surface to the length of the rod, which simplifies to (radius * twist angle) / length.

4 Medium

4 of 123

Remembering +4 | -1

The relationship between Young’s modulus

Y

, Bulk modulus

\mathrm{K}

and modulus of rigidity

\eta

View answer and explanation

Correct option: A

Y = \frac{{9\eta K}}{{\eta + 3K}}

Option A (

Y = \frac{{9\eta K}}{{\eta + 3K}}

) is correct because it is the standard formula relating Young's modulus (Y), Bulk modulus (K), and modulus of rigidity (

\eta

5 Medium

5 of 123

Application +4 | -1

Four wires of the same material are stretched by the same load. Which one of them will elongate most if their dimensions are as follows

View answer and explanation

Correct option: A

L = 100 cm, r = 1mm

Option A (L = 100 cm, r = 1mm) will elongate most because elongation is proportional to length and inversely proportional to the area (square of the radius).

6 Medium

6 of 123

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 doubling the radius quadruples the area, but the wire can bear four times the *load*, not stress.

7 Medium

7 of 123

Remembering +4 | -1

The modulus of rigidity is also known as:

View answer and explanation

Correct option: C

Shear modulus

Shear modulus (Option C) is correct because it measures a material's resistance to deformation by shear stress.

8 Medium

8 of 123

Analyzing +4 | -1

Which of the following relations is true

View answer and explanation

Correct option: D

\sigma = \frac{{0.5Y - \eta }}{\eta }

Option D (

\sigma = \frac{{0.5Y - \eta }}{\eta }

) is correct because it represents the correct relationship between Poisson's ratio (

\sigma

), Young's modulus (Y), and shear modulus (

\eta

9 Medium

9 of 123

Understanding +4 | -1

In a wire stretched by hanging a weight from its end, the elastic potential energy per unit volume in terms of longitudinal strain

\sigma

and modulus of elasticity

Y

View answer and explanation

Correct option: A

\frac{{Y{\sigma ^2}}}{2}

Option A (

\frac{{Y{\sigma ^2}}}{2}

) is correct because it represents the elastic potential energy per unit volume in terms of longitudinal strain and modulus of elasticity.

10 Medium

10 of 123

Analyzing +4 | -1

Statement-I: If the volume of a body remains unchanged, When subjected to tensile strain, the value of Poisson's ratio is

1 / 2

Statement-II: Phosphor bronze has low Young's modulus and high rigidity modulus

View answer and explanation

Correct option: B

Statement I is true and statement II is false

Statement I is true because when volume is unchanged under tensile strain, Poisson's ratio is 0.5. Statement II is false because phosphor bronze has high Young's modulus and low rigidity modulus.

11 Medium

11 of 123

Understanding +4 | -1

Liquids have no Poisson's ratio, because

View answer and explanation

Correct option: A

They have no definite shape

Option A is correct because liquids, unlike solids, do not maintain a fixed shape and readily conform to the shape of their container.

12 Medium

12 of 123

Understanding +4 | -1

If Poisson’s ratio

\sigma

- \frac{1}{2}

for a material, then the material is

View answer and explanation

Correct option: A

Uncompressible

Option A (Uncompressible) is correct. A Poisson's ratio of -1/2 indicates that the material maintains a constant volume under deformation, hence it's uncompressible.

13 Medium

13 of 123

Remembering +4 | -1

Which of the following substances has the highest elasticity?

View answer and explanation

Correct option: B

Steel

Option B is correct because steel has the highest elasticity among the given options, meaning it returns to its original shape most readily after deformation.

14 Medium

14 of 123

Application +4 | -1

When a weight of

10\,kg

is suspended from a copper wire of length 3 metres and diameter

0.4\,mm

, its length increases by

2.4\,cm

. If the diameter of the wire is doubled, then the extension in its length will be

View answer and explanation

Correct option: D

0.6\,cm

Option D (

0.6\,cm

) is correct because the extension is inversely proportional to the square of the diameter.

15 Medium

15 of 123

Analyzing +4 | -1

Assertion: If pressure is increased, bulk modulus of gases will increase.

Reason: With increase in pressure, temperature of gas also increases.

View answer and explanation

Correct option: C

If Assertion is true, but the Reason is false

Option C (If Assertion is true, but the Reason is false) is correct because while bulk modulus of gases increases with pressure, the reason provided about temperature increase is not always true or the primary reason.

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16 Medium

16 of 123

Application +4 | -1

Steel and copper wires of same length are stretched by the same weight one after the other. Young’s modulus of steel and copper are

2 \times {10^{11}}N/{m^2}\,and\,1.2 \times {10^{11}}N/{m^2}

. The ratio of increase in length

View answer and explanation

Correct option: B

\frac{3}{5}

Option B is correct. The ratio of increase in length is inversely proportional to the Young's modulus, given the same force, length, and area.

17 Medium

17 of 123

Application +4 | -1

A steel rail of length 5 m and area of cross-section

40\mathrm{ }c{m^3}

is prevented from expanding along its length while the temperature rises by

{10^0}C

. If coefficient of linear expansion and Young’s modulus of steel are

1.2\mathrm{ } \times \,\,{10^{ - 5}}{K^{ - 1}}

and

2\mathrm{ } \times \mathrm{ }{10^{11}}N{m^{ - 2}}

respectively, the force developed in the rail is approximately :

View answer and explanation

Correct option: B

1\mathrm{ } \times \mathrm{ }{10^5}N

Option B (

1\mathrm{ } \times \mathrm{ }{10^5}N

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

18 Medium

18 of 123

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 isothermal elasticity is always less than adiabatic elasticity.

19 Medium

19 of 123

Application +4 | -1

A rectangular bar

2\,\,cm

in breadth and

1\,\,cm

in depth and

100\,\,cm

in length is supported at its ends and a load of

2

kg is applied at its middle. If Young’s modulus of the material of the bar is

20\,\, \times \,\,{10^{11}}\,\,\mathrm{dyne c}{\mathrm{m}^{ - 2}},

, the depression in the bar is

View answer and explanation

Correct option: C

0.1225{\mkern 1mu} {\mkern 1mu} \,cm

Option C is correct. The depression in the bar is calculated using the formula for the deflection of a rectangular beam supported at its ends with a load at the center.

20 Medium

20 of 123

Application +4 | -1

A spherical ball contract in volume by

0.01\%

when subjected to normal uniform pressure of 100 atmosphere. What is the bulk modulus of elasticity of the material of the ball ? ( Take 1 atmosphere

{10^6}\mathrm{\;dyne\;c}{\mathrm{m}^{ - 3}})

View answer and explanation

Correct option: C

{10^{12}}\mathrm{\;dyne\;c}{\mathrm{m}^{ - 2}}

Option C (

{10^{12}}\mathrm{\;dyne\;c}{\mathrm{m}^{ - 2}}

) is correct because it is calculated using the bulk modulus formula with the given pressure and volume change.

21 Medium

21 of 123

Remembering +4 | -1

The Bulk modulus for an incompressible liquid is

View answer and explanation

Correct option: C

Infinity

Option C is correct because an incompressible liquid has an infinite bulk modulus, as it requires infinite pressure to change its volume.

22 Medium

22 of 123

Application +4 | -1

If a bar is made of copper whose coefficient of linear expansion is one and a half times that of iron, the ratio of the force developed in the copper bar to the iron bar of identical lengths and cross-sections, when heated through the same temperature range (Young’s modulus for copper may be taken equal to that of iron) is

View answer and explanation

Correct option: A

\frac{3}{2}

Option A (

\frac{3}{2}

) is correct because the force developed is proportional to the coefficient of linear expansion, and the coefficient of copper is 1.5 times that of iron.

23 Medium

23 of 123

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 the formula

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

24 Medium

24 of 123

Remembering +4 | -1

Under elastic limit the stress is

View answer and explanation

Correct option: B

Directly proportional to strain

Option B (Directly proportional to strain) is correct because Hooke's Law states that stress is directly proportional to strain within the elastic limit.

25 Medium

25 of 123

Remembering +4 | -1

Energy stored in stretching a string per unit volume is

View answer and explanation

Correct option: A

\frac{1}{2}\,\, \times \,\,\mathrm{stress}\,\, \times \mathrm{strain}

Option A is correct because the energy stored per unit volume in stretching a string is given by half the product of stress and strain.

26 Medium

26 of 123

Understanding +4 | -1

A rod elongated by

l

when a body of mass

M

is suspended from it. The work done is

View answer and explanation

Correct option: B

\frac{1}{2}M\mathrm{g}l

Option B (

\frac{1}{2}M\mathrm{g}l

) is correct because the work done is equal to the average force multiplied by the displacement.

27 Medium

27 of 123

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 area, which is proportional to the square of the diameter.

28 Medium

28 of 123

Analyzing +4 | -1

A: Bulk modulus for a perfectly plastic body is zero.
R: For perfect plastic material, there is no restoring force.

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 a perfectly plastic body experiences permanent deformation without restoring force.

29 Medium

29 of 123

Understanding +4 | -1

The work done in deforming body is given by

View answer and explanation

Correct option: B

\frac{1}{2}\left( {\mathrm{stress}\,\, \times \,\mathrm{strain}} \right)

Option B (

\frac{1}{2}\left( {\mathrm{stress}\times \\,\mathrm{strain}} \right)

) is correct because it represents the work done in deforming a body, which is equal to the elastic potential energy stored.

30 Medium

30 of 123

Analyzing +4 | -1

A: It is the breaking stress and not the breaking strength which depends on the material
R: Breaking strength

=\frac{\text {Breaking stress}}{\text {Area}}

View answer and explanation

Correct option: D

If both A and R are false

Option D (If both A and R are false) is correct because breaking stress depends on the material, and breaking strength is not simply breaking stress divided by area.

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