Elasticity

The stress-strain graph of two wires $A$ and $B$ is shown in the figure. If $Y_A$ and $Y_B$ are Young's moduli of materials of wires $A$ and $B$ respectively, then

If the given graph shows the load $(W)$ attached to and the elongation ( $\Delta l$ )produced in a wire of length one metre and area of cross-section $1 \mathrm{~mm}^2$, then the Young's modulus of the material of the wire is

The elastic potential energy stored in a copper rod of length one metre and area of cross-section $1 \mathrm{~mm}^2$ when stretched by 1 mm is
(Young's modulus of copper $=1.2 \times 10^{11} \mathrm{Nm}^{-2}$ )

A wire of length 0.5 m and area of cross-section $4 \times 10^{-6} \mathrm{~m}^2$ at a temperature of $100^{\circ} \mathrm{C}$ is suspended vertically by fixing its upper end to the ceiling. The wire is then cooled to $0^{\circ} \mathrm{C}$...

A wire is stretched 1 mm by a force $F$. If a second wire of same material, same length and 4 times the diameter of the first wire is stretched by the same force $F$, then the elongation of the second wire is

If the pressure on a body is increased from 200 kPa to 250 kPa , the volume of the body decreases by $0.25 \%$. The compressibility of the material of the body is (in $\mathrm{m}^2 \mathrm{~N}^{-1}$ )

If the longitudinal strain of a stretched wire is $0.2 \%$ and the Poisson's ratio of the material of the wire is 0.3 , then the volume strain of the wire is

The force required to stretch a steel wire of area of cross-section $1 \mathrm{~mm}^2$ to double its length is
(Young's modulus of steel $=2 \times 10^{11} \mathrm{~N}-\mathrm{m}^{-2}$ )

When a wire made of material with Young's modulus $\gamma$ is subjected to a stress $S$, the elastic potential energy per unit volume stored in the wire is

When a sphere is taken to the bottom of a sea of depth 1 km , it contracts in volume by $0.01 \%$, then the Bulk modulus of the material of the sphere is
(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

When a wire of length ' $L$ ' clamped at one end is pulled by a force ' $F$ ' from the other end, its length increases by ' $L$ '. If the radius of the wire and the applied force were halved, then the increase in its length is

As shown in the figure, a light uniform rod $P Q$ of length 150 cm is suspended from the ceiling horizontally using two metal wires $A$ and $B$ tied to the ends of the rod. The ratios of the radii and the Young's moduli of the materials of ...

The work done on a wire of volume of $2 \mathrm{~cm}^3$ is $16 \times 10^2 \mathrm{~J}$. If the Young's modulus of the material of the wire is $4 \times 10^{12} \mathrm{Nm}^{-2}$. Then the strain produced in the wire is

The elongation of copper wire of cross-sectional area $3.5 \mathrm{~mm}^2$, in the figure shown, is
\(\left(Y_{\text {Copper }}=10 \times 10^{10} \mathrm{Nm}^{-2} \text { and } g=10 \mathrm{~ms}^{-2}\right)\)

A wire of length 100 cm and area of cross-section $2 \mathrm{~mm}^2$ is stretched by two forces of each 440 N applied at the ends of the wire in opposite directions along the length of the wire. If the elongation of the wire is 2 mm , the Y...

The elastic energy stored per unit volume in terms of longitudinal strain $\varepsilon$ and Young's modulus $Y$ is

A 4 kg stone attached at the end of a steel wire is being whirled at a constant speed $12 \mathrm{~ms}^{-1}$ in a horizontal circle. The wire is 4 m long with a diameter 2.0 mm and Young's modulus of the steel is $2 \times 10^{11} \mathrm{N...

When the load applied to a wire is increased from 5 kg wt to 8 kg wt . The elongation of the wire increases from 1 mm to 1.8 mm . The work done during the elongation of the wire is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

If the work done in stretching a wire by 1 min is 2 J . The work necessary for stretching another wire of satrs material but with double radius of cross-section and half the length by 1 mm is

Two copper wires $A$ and $B$ of lengths in the ratio $1: 2$ and diameters in the ratio $3: 2$ are stretched by foren in the ratio $3 : 1$. The ratio of the clastic potential energies stored per unit volume in the wires $A$ and $B$ is.

Two springs $A$ and $B$ fixed at the top and are stretched by 8 cm and 16 cm respectively, when loads of 20 N and 10 N suspended at the lower ends. The ratio of the spring constant of the springs $A$ and $B$ is

The maximum possible height of a mountain on earth is approximately
(elastic limit of mountain rock $=30 \times 10^7 \mathrm{Nm}^{-2}$, average density of mountain rock $=3 \times 10^3 \mathrm{kgm}^{-3}$, $g=10 \mathrm{~ms}^{-2}$ )

A spherical ball of volume $2000 \mathrm{~cm}^3$ is subjected to a hydraulic pressure of 15 atm . If the change in volume is $5 \times 10^{-2} \mathrm{~cm}^3$, the bulk modulus of the material of the spherical ball is
$$ \left(1 \mathrm{~at...

Two wires \(A\) and \(B\) of same cross-section are connected end to end. When same tension is created in both wires, the elongation in \(B\) wire is twice the elongation in \(A\) wire. If \(L_A\) and \(L_B\) are the initial lengths of the ...

Same tension is applied to the following four wires made of same material. The elongation is longest in

The Young's modulus of a rubber string of length \(12 \mathrm{~cm}\) and density \(1.5 ~\mathrm{kgm}^{-3}\) is \(5 \times 10^8 ~\mathrm{Nm}^{-2}\). When this string is suspended vertically, the increase in its length due to its own weight i...

Young's modulus of a wire is \(2 \times 10^{11} \mathrm{Nm}^{-2}\). If an external stretching force of \(2 \times 10^{11} \mathrm{~N}\) is applied to a wire of length \(L\). The final length of the wire is (cross-section = unity)