Question

A block of gelatin is $60mm$ by $60mm$ by $20mm$ when unstressed. A force of $0.245N$ is applied tangentially to the upper surface, causing a $5mm$ displacement relative to the lower surface. Following observations are made regarding the block.
$\left(i\right)$ the shearing stress develop on surface is $68.1pa$
$\left(ii\right)$ the shearing strain develop on surface is $0.25$
$\left(iii\right)$ the shear modulus of material is $274.4\frac{N}{M^2}$

• A.
  only statement $\left(i\right)$ and $\left(iii\right)$ are correct
  
• B.
  only statement $\left(i\right)$ and $\left(iii\right)$ are correct
  
• C.
  
  all the statements are correct
  
• D.
  only statement $\left(i\right)$ and $\left(ii\right)$ are correct
  

Answer 1

The correct option is C


all the statements are correct

Calculate shear stress of block

Given,
Size of block of gelatin $=60mm\times 60mm\times 20mm$
Force $=F=0.245N$
Stress $=\frac{F}{A}=\frac{0.245}{36\times {10}^4}=68.1pa$

Calculate shear strain of block

Given,
Displacement of upper surface with respect to ground, $r=5mm$
strain $=\theta =\frac{r}{h}=\frac{5}{20}=0.25$

Calculate shear modulus of block

shear modulus $=\frac{\frac{F}{A}}{\tan \theta }$
For small$\theta ,\tan \theta \approx \theta$
$\frac{68.1}{0.25}=272.4N/m^2$
Hence, all the values are correct as given in question.
Final answer: (d)