Hooke's Law and Modulus of Elasticity

A student performs an experiment to determine the Young’s modulus of a wire, exactly $2 \mathrm{m}$ long, by Searle’s method. In a particular reading, the student measures the extension in the length of the wire to be $0.8 \mathrm{mm}$ with an uncertainty of $\pm 0.05 \mathrm{mm}$ at a load of exactly $1.0 \mathrm{kg}$. The student also measures the diameter of the wire to be $0.4 \mathrm{mm}$ with an uncertainty of $\pm 0.01 \mathrm{mm}$. Take $g=9.8 \mathrm{m} {\mathrm{s}}^{-2}$ (exact). The Young’s modulus obtained from the reading is

If the Young's modulus of the material of a wire is numerically equal to ten times the stress applied to a wire of length $l$, then the change in the length of the wire is

The bulk modulus of a liquid is $3\times {10}^{10}{\mathrm{Nm}}^{-2}$. The pressure required to reduce the volume of liquid by $2\%$ is :

A steel wire of cross-sectional area $3\times {10}^{-6} {\mathrm{m}}^2$ can withstand a maximum strain of ${10}^{-3}$. Young's modulus of steel is $2\times {10}^{11} \mathrm{N} {\mathrm{m}}^{-2}$. The maximum mass this wire can hold is,

The backlash error can be eliminated in Searle's experiment, by rotating screw in

A copper and a steel wire of same diameter are connected end to end. A deforming force $F$ is applied to this composite wire which causes a total elongation of $1$ $\mathrm{cm}$. The two wires will have:

A Copper wire of length ${\mathrm{L}}_{\mathrm{Cu}}$, Young's modulus ${\mathrm{Y}}_{\mathrm{Cu}}$, and diameter $d$ is hung from the ceiling. An Aluminium wire of length ${\mathrm{L}}_{\mathrm{Al}}$, Young's modulus ${\mathrm{Y}}_{\mathrm{Al}}$, and of same diameter $d$ is joined end-to-end at the free end of the Copper wire. If under the action of a load applied at the free end of the Aluminium wire the net elongation is $∆L$, the applied load 

The dimensional formula for young's modulus is

One end of a wire of $8 \mathrm{mm}$ radius and $100 \mathrm{cm}$ length is fixed and the other end is twisted through an angle of $45°,$ The angle of shear is

The ratio of shearing stress to the corresponding shearing strain is called the modulus of _____.

The dimensional formula of modulus of rigidity is $M{L}^{-1}{T}^{-2}$.

State the units and dimensions of modulus of rigidity. 

The dimensional formula of modulus of rigidity is

A rubber ball is taken to a $100 \mathrm{m}$ deep lake and its volume changes by $0.1\%$. The bulk modulus of rubber is nearly

A steel rail of length $5 \mathrm{m}$ and area of cross-section $40\mathrm{ }{\mathrm{cm}}^2$ is prevented from expanding along its length while the temperature rises by $10 °\mathrm{C}$ . If coefficient of linear expansion and Young's modulus of steel are $1.2\times {10}^{-5}\mathrm{ }{\mathrm{K}}^{-1}$ and $2\times {10}^{11}\mathrm{ }\mathrm{N} {\mathrm{m}}^{-2}$ respectively, the force developed in the rail is approximately:

The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by 100^oC is :
(For steel Young's modulus is 2 x 10¹¹ N m^-2 and coefficient of thermal expansion is 1.1 x 10^-5 K^-1)

The pressure of a medium is changed from $1.01\times {10}^5\mathrm{\hspace{0.17em}}\mathrm{Pa}$ to $1.165\times {10}^5\mathrm{\hspace{0.17em}}\mathrm{Pa}$ and change in volume is $10\%$ keeping temperature constant. The bulk modulus of the medium is

A material has Poisson’s ratio $0.2$. If a uniform rod made out of it suffers longitudinal strain $4.0\times {10}^{–3}$, then calculate the percentage change in its volume.

A $15$ $\mathrm{kg}$ mass fastened to the end of the steel wire of unstretched length $1.0$ $\mathrm{m}$ is whirled in a vertical circle with an angular velocity of $2$ $\mathrm{rev}$ ${\mathrm{s}}^{–1}$. The cross-section of the wire is $0.05 {\mathrm{cm}}^2$. The elongation of the wire when the mass is at the lowest point of its path is: (Take $g=10 \mathrm{m}\mathrm{ }{\mathrm{s}}^{–2}$, $Y_{\mathrm{steel}}=2\times {10}^{11} \mathrm{N}\mathrm{ }{\mathrm{m}}^{–2}$ )

A wire of natural length $l$, Young's modulus Y and area of cross-section A is extended by $x$. Then the energy stored in the wire is given by