Question

A cube of green jelly rests on a table. A lateral force of $30\text{N}$ is applied and the jelly tilts as shown in the figure. Choose the correct option(s).

• A. Shear strain induced is $1.25$
• B. Shear modulus is $1511.11{\text{N/m}}^2$
• C. Shear strain induced is $0.58$
• D. Shear modulus is $1111.11{\text{N/m}}^2$

Answer 1

Answer: (C), (D)

The correct options are
C Shear strain induced is $0.58$
D Shear modulus is $1111.11{\text{N/m}}^2$

Let the edge length of cube be $x$.


In $\Delta ABC$,
$\tan {30}^{\circ }=\frac{0.125}{x}$
$\Rightarrow x=\frac{0.125}{\tan {30}^{\circ }}=0.125\times \sqrt{3}$
$\Rightarrow x=0.216\text{m}...\left(1\right)$

Shear strain $=\frac{\Delta L}{L}$
$\Rightarrow$ Shear strain $=\frac{0.125}{0.216}=0.58$

For Shear modulus,
$G=\frac{\text{shear stress}}{\text{shear strain}}=\frac{\frac{F}{A}}{\frac{\Delta L}{L}}$

$\Rightarrow G=\frac{FL}{A\Delta L}$
$G=\frac{30\times 0.216}{(0.216{)}^2\times 0.125}$
$F=30\text{N}$, given
$\therefore G=1111.11{\text{N/m}}^2$