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JEE Main
Exam
JEE Main
Subject
Physics
Chapter
Mechanical Properties of Solids

JEE Main · Physics · Mechanical Properties of Solids

A rubber cube of side 5 ~cm has one face fixed, while a tangential...

A rubber cube of side 5 cm5 \mathrm{~cm} has one face fixed, while a tangential force 1800 N1800 \mathrm{~N} is applied on its opposite face. If modulus of rigidity of rubber is 2.4×106Nm−22.4 \times 10^6 \mathrm{Nm}^{-2}, then the lateral displacement of the strained face is ________

Options

  1. A3 mm
  2. B5 mm
  3. C15 mm
  4. D1.5 mm

Correct answer

C. 15 mm

Step-by-step solution

Shear stress = Tangential force  Area =1800 N(0.05)2\frac{\text { Tangential force }}{\text { Area }}=\frac{1800 \mathrm{~N}}{(0.05)^2}Shear strain =tan⁡θ=\tan \theta=xh= Lateral displacement  Height of cube =x5 cm=x m0.05 m\begin{aligned}& =\frac{x}{h}=\frac{\text { Lateral displacement }}{\text { Height of cube }}=\frac{x}{5} \mathrm{~cm}\\ & =\frac{x \mathrm{~m}}{0.05 \mathrm{~m}} \end{aligned}Modulus of rigidity, \eta=$\frac{\text { Shear stress }}{\text { Shear strain }}$2.4 $\times$10^6 $\frac{\mathrm{N}}{\mathrm{m}^2}=\frac{1800}{25 \times 10^{-4}} \times \frac{0.05}{x} \mathrm{~N}$/ $\mathrm{m}^2 or\begin{aligned}x \text{ and } =\frac{1800 \times 0.05}{25 \times 10^{-4} \times 2.4 \times 10^6}\\ \text{ and } =15 \times10^{-3} \mathrm{~m}\\ \text{ and } =15 \mathrm{~mm} \end{aligned}$$
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