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 $0^{\circ} \mathrm{C}$, but is prevented from contracting by attaching a mass at the lower end. If the mass of the wire is negligible, then the value of the mass attached to the wire is

[Young's modulus of material of the wire $=10^{11} \mathrm{Nm}^{-2}$, coefficient of linear expansion of the material of the wire $=10^{-5} \mathrm{~K}^{-1}$ and acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ ]

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 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

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 $\mathrm{m}^2 \mathrm{~N}^{-1}$ )

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

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 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

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 $=10 \mathrm{~ms}^{-2}$ )

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 two wires $A$ and $B$ are respectively $2: 3$ and $3: 2$. The position at which a weight should be suspended from the rod such that the elongations of the two wires become equal is

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 Young's modulus of the material of the wire is

The elongation of copper wire of cross-sectional area $3.5 \mathrm{~mm}^2$, in the figure shown, is

$$ \left(Y_{\text {Copper }}=10 \times 10^{10} \mathrm{Nm}^{-2} \text { and } g=10 \mathrm{~ms}^{-2}\right) $$

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 $=10 \mathrm{~ms}^{-2}$ )

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 wires $$A$$ and $$B$$ respectively, then (Young's modulus of material of wire $$A=2 \times 10^{11} \mathrm{~Nm}^{-2}$$ and Young's modulus of material of wire $$B=1.1 \times 10^{11} \mathrm{~Nm}^{-2}$$).

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

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)

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 is (Take, $$g=10 \mathrm{~ms}^{-2}$$ )