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

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

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

A cube of side ${\rm{40}}\,\,{\rm{mm}}$ has its upper face displaced by ${\rm{0}}.{\rm{1}}\,{\rm{mm}}$ by a tangential force of ${\rm{8}}\,\,{\rm{kN}}$. The shearing modulus of cube is

$2\,\, \times {10^9}\,{\rm{N}}{{\rm{m}}^{ - 2}}$

$4\,\, \times {10^9}\,{\rm{N}}{{\rm{m}}^{ - 2}}$

$8\,\, \times {10^9}\,{\rm{N}}{{\rm{m}}^{ - 2}}$

$16\,\, \times {10^9}\,{\rm{N}}{{\rm{m}}^{ - 2}}$

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NEET • PHYSICS • MECHANICAL PROPERTIES OF SOLIDS

Mechanical properties of solids practice · Mixed difficulty

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Showing 1-30 of 177 questions

1 Easy

1 of 177

Application +4 | -1

A 20 kg load is suspended by a wire of area of cross section is

1\,m{m^2}

. The stress produced in

N/{m^2}

\left[ {g = 10\,m{s^{ - 2}}\,} \right]\,

View answer and explanation

Correct option: B

2 \times {10^8}

Option B (

2 \times {10^8}

) is correct because stress is calculated as force divided by area, where the force is the weight of the load (20 kg * 10 m/s²) and the area is 1 mm² converted to m².

2 Medium

2 of 177

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.

3 Easy

3 of 177

Application +4 | -1

A wire extends by

\mathrm{1 mm}

when a force is applied. Double the force is applied to another wire of same material and length but half the radius of cross-section. The elongation of the wire in mm will be

View answer and explanation

Correct option: A

\mathrm{8}

Option A (8) is correct because elongation is inversely proportional to the area and directly proportional to the force.

4 Medium

4 of 177

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.

5 Medium

5 of 177

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.

6 Medium

6 of 177

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

7 Medium

7 of 177

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).

8 Medium

8 of 177

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.

9 Medium

9 of 177

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.

10 Medium

10 of 177

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

11 Easy

11 of 177

Application +4 | -1

A cube of side

\mathrm{40}\,\,\mathrm{mm}

has its upper face displaced by

\mathrm{0}.\mathrm{1}\,\mathrm{mm}

by a tangential force of

\mathrm{8}\,\,\mathrm{kN}

. The shearing modulus of cube is

View answer and explanation

Correct option: A

2\,\, \times {10^9}\,\mathrm{N}{\mathrm{m}^{ - 2}}

Option A (

2 \times {10^9}\,\mathrm{N}{\mathrm{m}^{ - 2}}

) is correct because it is the result of calculating the shearing modulus using the given values of tangential force, area, and displacement.

12 Easy

12 of 177

Understanding +4 | -1

The elastic potential energy of a stretched wire is given by

View answer and explanation

Correct option: B

U=\frac{A Y}{2 L} l^2

Option B (

U=\frac{A Y}{2 L} l^2

) is correct because it represents the formula for elastic potential energy stored in a stretched wire.

13 Medium

13 of 177

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.

14 Medium

14 of 177

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.

15 Easy

15 of 177

Application +4 | -1

A metal cube of side 8 cm. If the top of the cube is displaced by 0.04 cm with respect to its bottom. What is the shearing stress if the rigidity modulus is

4 \times {10^6}\,N/{m^2}\,\,\left[ {\mathrm{in}\,\,N/{m^2}} \right]

View answer and explanation

Correct option: B

2 \times {10^4}

Option B (

2 \times {10^4}

) is correct because shearing stress is the product of the rigidity modulus and the shearing strain.

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16 Medium

16 of 177

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.

17 Medium

17 of 177

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.

18 Medium

18 of 177

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.

19 Easy

19 of 177

Application +4 | -1

A wire of 4 m length 16 mm radius is clamped at upper end. The lower end is twisted by an angle of

30^\circ

. The angle of shear is

View answer and explanation

Correct option: C

0.12^\circ

Option C (

0.12^\circ

) is correct because the angle of shear is calculated by dividing the arc length at the wire's surface by the wire's length.

20 Medium

20 of 177

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.

21 Medium

21 of 177

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.

22 Hard

22 of 177

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.

23 Medium

23 of 177

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.

24 Easy

24 of 177

Application +4 | -1

The interatomic distance for a metal is

3 \times 10^{-10} \mathrm{~m}

. If the interatomic force constant is

3.6 \times 10^{-9} \mathrm{~N} / \mathop {\text{A}}\limits^ \circ

, then the Young's modulus (in

\mathrm{Nm}^{-2}

) will be

View answer and explanation

Correct option: A

1.2 \times 10^{11}

Option A (

1.2 \times 10^{11}

) is correct because Young's modulus is calculated from the interatomic force constant and distance.

25 Easy

25 of 177

Application +4 | -1

Young's modulus of rubber is

10^4 \mathrm{~N} / \mathrm{m}^2

and area of cross-section is

2 \mathrm{~cm}^2

. If force of

2 \times 10^5

dynes is applied along its length, then its initial length

L

becomes

View answer and explanation

Correct option: C

Option C (2L) is correct because the final length is twice the initial length based on the given Young's modulus, area, and force.

26 Medium

26 of 177

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.

27 Medium

27 of 177

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.

28 Medium

28 of 177

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.

29 Medium

29 of 177

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.

30 Medium

30 of 177

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.

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