A rubber cube of side 5 cm has one face fixed while a tangential force 1800N is applied on its opposite face. If modulus of rigidity of rubber is `2.4 xx 10^(6) Nm^(-2)`, then the lateral displacement of the strained face is _____

Options

A. 3mm
B. 5mm
C. 15mm
D. 1.5mm

Answer

C

Explanation

Shear stress `=("Tangential force")/("Area") = (1800N)/((0.05)^(2))`
Shear strain =`tan theta = (x)/(h) = ("Lateral displacement")/("Height of cube") = (x)/(5) cm`
`= (x m)/(0.05m)`
Modulus of rigidity, `eta = ("Shear stress")/("Shear strain")`
`2.4 xx 10^(6) (N)/(m^(2)) = (1800)/(25 xx 10^(-4)) xx (0.05)/(x) N//m^(2)`
or `x = (1800 xx 0.05)/(25 xx 10^(-4) xx 2.4 xx 10^(6))`
`=15 xx 10^(-3)m`
=15mm