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

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:

In practice, Poisson’s ratio $\sigma$ lies between

Young's modulus of a perfectly rigid body is

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 

Which of the following relation between elastic constants is true?

The dimensional formula for young's modulus is

Which one of the following is true about Bulk Modulus of elasticity?
 

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 Bulk modulus $\left(K\right)$ of a material having young's modulus $\left(E\right)$ $=$$200 \mathrm{GPa}$  and modulus of rigidity $\left(G\right)=80 \mathrm{GPa}$.

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

A solid sphere of radius $r$ made of a soft material of bulk modulus $K$ is surrounded by a liquid in a cylindrical container. A massless piston of area $a$ floats on the surface of the liquid, covering an entire cross-section of the cylindrical container. When a mass $m$ is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere $\left(\frac{dr}{r}\right)$ , is: