Physics

Solid Mechanics

510 Questions

Solid mechanics questions evaluate the understanding of stress, strain, and material deformation under various loads. Topics include analyzing beams, cantilevers, and structural steel designs using specific industrial standards. These principles are strictly examined in engineering and civil services preliminary tests.

Stress and strainBeam analysisPrestressed concreteMaterial strengthStructural design

Solid Mechanics Questions

Multiple choice physics mechanical properties of solids applications of elasticity elastic energy properties of matter

The buckling of a beam is found to be more if __________.

  1. The breadth of the beam is large

  2. The beam material has large value of Young's modulus

  3. The length of the beam is small

  4. The depth of the beam is small
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Critical buckling stress of a column formula is given by 

$\sigma=\dfrac{F}{A}=\dfrac{{\pi}^2 r^2 E}{L^2}$
where $\sigma$ = critical stress
$L$= unsupported length of the column
$r=$ least radius 
So if the depth of the beam i small, buckling of a beam will be more.

Multiple choice physics properties of material substances poisson ratio poisson's ratio elastic energy

Which of the following statements is correct regarding Poisson's ratio?

  1. It is the ratio of the longitudinal strain to the lateral strain

  2. Its value is independent of the nature of the material

  3. It is unitless and dimensionless quantity
  4. The practical value of Poisson's ratio lies between $0$ and $1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The ratio of the lateral strain to longitudinal strain is called Poisson's ratio.
Hence, option (a) is an incorrect statement.
Its value depends only on the nature of the material. 
Hence, option (b) is an incorrect statement.
It is the ratio of two like physical quantities.
Therefore, it is unitless and dimensionless quantity.
Hence option (c) is a correct statement
The practical value of Poisson's ratio lies between $0$ and $0.5$
hence option (d) is an incorrect statement.

Multiple choice physics properties of material substances poisson ratio poisson's ratio elastic energy

A material has Poisson's ratio $0.2$. If a uniform rod of its suffers longitudinal strain $4.0\times {10}^{-3}$, calculate the percentage change in its volume.

  1. $0.15$%
  2. $0.02$%
  3. $0.24$%
  4. $0.48$%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given:
 Poisson's ratio $0.2$. 
 longitudinal strain $4.0\times 10^{−3}$
As $\sigma =-\cfrac { \Delta R/R }{ \Delta l/l } $
$\therefore \cfrac { \Delta R }{ R } =-\sigma \cfrac { \Delta l }{ l } =-0.2\times 4.0\times { 10 }^{ -3 }=-0.8\times { 10 }^{ -3 }\quad $
$V=\pi { R }^{ 2 }l$
$\therefore \cfrac { \Delta V }{ V } \times 100=\left( 2\cfrac { \Delta R }{ R } +\cfrac { \Delta l }{ l }  \right) \times 100=\left[ 2\times \left( -0.8\times { 10 }^{ -3 } \right) +4.0\times { 10 }^{ -3 } \right] \times 100=2.4\times { 10 }^{ -3 }\times 100=0.24$%

Multiple choice physics properties of material substances poisson ratio poisson's ratio elastic energy

For a given material, the Young's modulus is $2.4$ times that of the modulus of rigidity. Its Poisson's ratio is

  1. $2.4$
  2. $1.2$
  3. $0.4$
  4. $0.2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

As  $Y=2\eta \left( 1+\sigma  \right) $
where the symbols have their usual meanings
Given: $Y=2.4\eta $
$\therefore 2.4\eta =2\eta \left( 1+\sigma  \right) $
$1.2=1+\sigma \quad or\quad \sigma 1.2-1=0.2$

Multiple choice physics properties of material substances poisson ratio poisson's ratio elastic energy

For perfectly rigid bodies, the elastic constants Y, B and n are 

  1. Y=B=n =0

  2. Y=B=n =infinity

  3. Y=2B=3n

  4. Y=B=n =0.5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Perfectly rigid bodies cannot be deformed upon application of any amount of force. Thus, strain is zero or the modulus of elasticity which is inversely proportional to strain becomes infinity

Thus option (b) is the correct option

Multiple choice physics properties of material substances poisson ratio poisson's ratio elastic energy

A material has poisson's ratio 0.5. If a uniform rod of it suffers a longitudinal strain of $3\times { 10 }^{ -3 }$, what will be percentage increase in volume?

  1. 2%

  2. 3%

  3. 5%

  4. 0%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Here, $E=3k(1-2\mu)$

where, $E=$Modulus of elasticity
$\mu=$Poisson's ratio
$k=$Modulus of elasticity
Here, $\mu=0.5$ then $k\longrightarrow \infty $
$k=\cfrac { \Delta P }{ \left( \cfrac { \Delta V }{ V }  \right)  } $
If $k\longrightarrow \infty $, then $\Delta V\longrightarrow 0$.
Hence the percentage change in volume$=0\%$

Multiple choice physics properties of material substances poisson ratio poisson's ratio elastic energy

When a body undergoes a linear tensile strain if experience a lateral contraction also. The ratio of lateral contraction to longitudinal strain is known as

  1. Young's modulus

  2. Bulk modulus

  3. Poisson's law

  4. Hooke's law
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Poisson's ratio is the ratio of transverse contraction strain to longitudinal extension strain in the direction of stretching force

Multiple choice physics properties of material substances poisson ratio poisson's ratio elastic energy

A compressive force is applied to a uniform rod of rectangular cross-section so that its length decreases by $1\%$. If the Poisson’s ratio for the material of the rod be $0.2$, which of the following statements is correct ? The volume approximately .....”

  1. decreases by $1\%$
  2. decreases by $0.8\%$
  3. decreases by $0.6\%$
  4. increases by $0.2\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$V=Al=abl; \dfrac{\triangle a}{a}=\dfrac{\triangle b}{b}\left[\because \sigma=\dfrac{\dfrac{-\triangle a}{a}}{\dfrac{\triangle l}{l}}=\dfrac{\dfrac{\triangle b}{b}}{\dfrac{\triangle l}{l}}\right]$
$\Rightarrow \dfrac{\triangle V}{V}=2\dfrac{\triangle a}{a}+\dfrac{\triangle I}{l}=-2\sigma \dfrac{\triangle I}{I}+\dfrac{\triangle I}{I}\Rightarrow \dfrac{\triangle V}{V}=\dfrac{\triangle I}{I}(1-2\sigma)-1(1-2\times 0.2)=-1(1-0.4)=-0.6$
$\because$ The volume approximately decreases by $0.6\%$.

Multiple choice physics properties of material substances poisson ratio poisson's ratio elastic energy

When a rubber cord is stretched, the change in volume is negligible compared to the change in its linear dimension. Then poisson's ratio for rubber is

  1. infinite

  2. zero

  3. 0.5

  4. -1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

By Lame's relation, $\ \nu = \dfrac { 1 }{ 2 } -\dfrac { E  }{ 6B} ,$ where  $B$ is bulk modulus.
Given, volume change is negligible, thus B tends to infinity. $(B=-V\dfrac { dP }{ dV } )$
 Thus, $\nu=\dfrac { 1 }{ 2 } $

Multiple choice physics properties of material substances poisson ratio poisson's ratio elastic energy

Poisson' ratio is defined as the ratio of 

  1. longitudinal stress and longitudinal strain

  2. longitudinal stress and lateral stress

  3. lateral stress and longitudinal stress

  4. lateral stress and lateral strain
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Poisson' ratio is defined as the ratio of lateral stress and longitudinal stress

The correct option is (c)

Multiple choice physics properties of material substances poisson ratio poisson's ratio elastic energy

The change in unit volume of a material under tension with increase in its poisson's ratio will be

  1. Increase

  2. Decrease

  3. Remains same

  4. Initially increases and then decreases
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The poisson's ratio is related to modulus of elasticity as $Y = 3B(1-2 \sigma)$. Since stress is same for Y and B, we get, $dL/L=dV/3V(1-2 \sigma) \implies dV=3V (dL/L)(1-2 \sigma)$
As $\sigma$ is increased, $dV$ decreases. 

The correct option is (b)

Multiple choice physics properties of material substances poisson ratio poisson's ratio elastic energy

The theoretical limits of poisson's ratio lies between -1 to 0.5 because

  1. Shear modulus and bulk's modulus should be positive

  2. Bulk's modulus is negative during compression

  3. Shear modulus is negative during compression

  4. Young's modulus should be always positive
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let Y, K, n and $\sigma$ be the Young's Modulus, Bulk modulus, Modulus of Rigidity and Poisson's Ratio, respectively. 
Y = 3K (1 - 2$\sigma$) [Standard formula] 
Y = 2n (1 + $\sigma$) [Standard formula] 
Hence, 3K (1 - 2$\sigma$) = 2n (1 + $\sigma$) 
Now K and n are always positive, so 
i) If $\sigma$ be +ve, then RHS is always +ve. So LHS must also be +ve. Therefore, 2$\sigma$ < 1 or $\sigma$ <1/2 
ii) If $\sigma$ be -ve, then LHS will always be +ve. Therefore, 1+$\sigma$ > 0 or $\sigma$ > -1 
Thus the limiting values of Poisson's ratio are -1 < $\sigma$ < 1/2

The correct option is (a)