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 properties of material substances poisson ratio poisson's ratio elastic energy

For a material $Y={ 6.6\times 10 }^{ 10 }\ { N/m }^{ 2 }$ and bulk modulus $K{ 11\times 10 }^{ 10 }\ { N/m }^{ 2 }$, then its Poisson's ratio is:

  1. $0.8$
  2. $0.35$
  3. $0.7$
  4. $0.4$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given that,

Young’s modulus $Y=6.6\times {{10}^{10}}\,N/{{m}^{2}}$

Bulk modulus $B=11\times {{10}^{10}}\,N/{{m}^{2}}$

We know that,

  $ Y=3K\left( 1-2\mu  \right) $

 $ 6.6\times {{10}^{10}}=3\times 11\times {{10}^{10}}-66\times {{10}^{10}}\mu  $

 $ -\mu =\dfrac{\left( 6.6-33 \right)\times {{10}^{10}}}{66\times {{10}^{10}}} $

 $ \mu =0.4 $

Hence, the poisson’s ratio is $0.4$

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 $2\times { 10 }^{ -3 }$, then the percentage increase in its volume is 

  1. 0%

  2. 10%

  3. 20%

  4. 5%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volumetric strain = longitudinal_strain * (1 - 2*sigma). If sigma = 0.5, then (1 - 2*0.5) = 0, so the volume change is 0%.

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

Volumetric strain = longitudinal_strain * (1 - 2*sigma). Since sigma = 0.5, (1 - 2*0.5) = 0, so the volume change is 0%.

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

what is the ratio of Youngs modulus $E$ to shear modulus $G$ in terms of poissons ratio$?$

  1. $2\left( {1 + \mu } \right)$
  2. $2\left( {1 - \mu } \right)$
  3. $\frac{1}{2}\left( {1 - \mu } \right)$
  4. $\frac{1}{2}\left( {1 + \mu } \right)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

As we know$:-$

$G = \frac{E}{{2\left( {1 + \mu } \right)}}$ 
so this gives the ratio of $E$ to $G = 2\left( {1 + \mu } \right)$
Hence,
option $(A)$ is correct answer.

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 its modulus of rigidity. Its Poisson's ratio is

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

$Y = 2\eta \left( {1 + \sigma } \right)$

But $Y = 2.4\eta $
$\therefore 2.4\eta  = 2\eta \left( {1 + \sigma } \right)$
$\left( {1 + \sigma } \right) = 1.2$
$\sigma  = 0.2$
Hence,
option $(A)$ is correct answer.

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

Which of the following pairs is not correct?

  1. strain-dimensionless
  2. stress-$N/m^{2}$
  3. modulus of elasticity-$N/m^{2}$
  4. poisson's ratio-$N/m^{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

stress is $\dfrac{F}{A}$ hence unit $N/m^2$

strain is $\dfrac{\Delta l}{L}$ so unit $m/m$ therefore dimensionless
modulus of elasticity is $ \dfrac{stress}{strain}$ hence same unit  as stress as the denominator is dimensionless
poisson's ratio $\dfrac{-\epsilon _t}{\epsilon _l} $ so its also going to be dimensionless

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

A uniform bar of length 'L' and cross sectional area 'A' is subjected to a tensile load 'F'. 'Y' be the Young modulus and '$\sigma$' be the Poisson's ratio then volumetric strain is  

  1. $\frac{F}{AY}(1 - \sigma)$
  2. $\frac{F}{AY}(2 - \sigma)$
  3. $\frac{F}{AY}(1 - 2\sigma)$
  4. $\frac{F}{AY} \sigma$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volumetric strain is defined as the change in volume divided by the original volume. For a bar under uniaxial stress, the longitudinal strain is F/(AY) and the lateral strains are -sigma * F/(AY). Summing these gives the volumetric strain: F/(AY) * (1 - 2*sigma).

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

Ratio of transverse to axial strain is 

  1. Toricelli ratio

  2. Poisson's ratio

  3. Stoke's ratio

  4. Bernoulli's ratio
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Hookes law states that stress is proportional to strain up to elastic limit. If p is the stress induced in material and e the corresponding strain, then according to Hooke's law, 
$\dfrac{P}{E}$ = E, a constant.

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

Consider the statements A and B, identify the correct answer given below :
(A) : If the volume of a body remains unchanged when subjected to tensile strain, the value of poisson's ratio is 1/2.
(B) : Phosper bronze has low Young's modulus and high rigidity modulus. 

  1. A and B are correct

  2. A and B are wrong

  3. A is correct and B is wrong

  4. A is wrong and B is right
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Experimental value of poisson's ratio is always between $0$ to $1/2$ .

As Phosper bronze is solid so, value of young's modulus is also high.

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

For a material Y $=$ 6.6x10$^{10}$ N/m$^{2}$ and bulk modulus K $=$ 11x10$^{10}$ N/m$^{2}$, then its Poissons's ratio is

  1. 0.8

  2. 0.35

  3. 0.7

  4. 0.4
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Relation  between  Young's  modulus,  bulk  modulus  and  poisson's  ratio  is  given  below :
$Y = 3B (1-2\sigma)$
So,  according  to  problem
$ 6.6 \times  10^{10} = 3 \times 11 \times 10^{10} (1-2\sigma)$
$ \sigma = 0.4$