The edge of an aluminium cube is 10; cm long. | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The shear modulus $\eta$ is defined as the ratio of shear stress to shear strain:$\eta = \frac{F/A}{\Delta L/L}$Where $F$ is the force applied,$A$

Vedclass · Accepted Answer

$3.92 	imes 10^{-7}\; m$

Vedclass · Answer

(C) The shear modulus $\eta$ is defined as the ratio of shear stress to shear strain:$\eta = \frac{F/A}{\Delta L/L}$Where $F$ is the force applied,$A$ is the area of the face,$L$ is the side length of the cube,and $\Delta L$ is the vertical deflection.Rearranging for $\Delta L$:$\Delta L = \frac{F L}{A \eta}$Given:$F = mg = 100\; kg 	imes 9.8\; m/s^2 = 980\; N$$L = 10\; cm = 0.1\; m$$A = L^2 = (0.1\; m)^2 = 0.01\; m^2 = 10^{-2}\; m^2$$\eta = 25\; GPa = 25 	imes 10^9\; Pa$Substituting the values:$\Delta L = \frac{980 	imes 0.1}{10^{-2} 	imes 25 	imes 10^9}$$\Delta L = \frac{98}{0.25 	imes 10^9} = 392 	imes 10^{-9}\; m = 3.92 	imes 10^{-7}\; m$The vertical deflection is $3.92 	imes 10^{-7}\; m$.

The edge of an aluminium cube is $10\; cm$ long. One face of the cube is firmly fixed to a vertical wall. $A$ mass of $100\; kg$ is then attached to the opposite face of the cube. The shear modulus of aluminium is $25\; GPa$. What is the vertical deflection of this face?

Similar Questions

$A$ wire of length $1 \text{ m}$ and radius $2 \text{ mm}$ is vertically clamped. The lower end is twisted through an angle of $45^{\circ}$. The angle of shear is $.....$ (in $^{\circ}$)

$A$ uniform wire of length $L$ and radius $r$ is twisted by an angle $\alpha$. If the modulus of rigidity of the wire is $\eta$,then the elastic potential energy stored in the wire is .........

$A$ steel rod is projecting out of a rigid wall. The shearing strength of steel is $345 \, MN/m^2$. The dimensions are $AB = 5 \, cm$ and $BC = BE = 2 \, cm$. The maximum load that can be put on the face $ABCD$ is .......... $kg$ (neglect bending of the rod). Take $g = 10 \, m/s^2$.

Two wires of the same length and same material have radii $r_1$ and $r_2$. Their one end is fixed,and when an equal torque is applied to the other end,what is the ratio of their angular displacement?

The units of modulus of rigidity are

Vedclass Test Series

Exam Paper Generator

Online Exam Module