The work to be done to produce a strain of $10^{-3}$ in a steel wire of mass 2.96 kg and density $7.4 \mathrm{~g} \mathrm{~cm}^{-3}$ is

(Young's modulus of steel $=2 \times 10^{11} \mathrm{Nm}^{-2}$ )

The Young's modulus and Poisson's ratio of a material are respectively $Y$ and $\sigma$. The force required to decrease the area of cross-section of a wire made of this material by $\triangle A$ is

A metal rod of area of cross-section $3 \mathrm{~cm}^2$ is stretched along its length by applying a force of $9 \times 10^4 \mathrm{~N}$. If the Young's modulus of the material of the rod is $2 \times 10^{11} \mathrm{Nm}^{-2}$, the energy stored per unit volume in the stretched rod is

Two wires $A$ and $B$ made of same material and areas of cross-section in the ratio $1: 2$ are stretched by same force. If the masses of the wires $A$ and $B$ are in the ratio $2: 3$, then the ratio of the elongations of the wires $A$ and $B$ is

If a brass sphere of radius 36 cm is submerged in a lake at a depth where the pressure is $10^7 \mathrm{~Pa}$, then the change in the radius of the sphere is

(Bulk modulus of brass $=60 \mathrm{GPa}$ )

A block of mass 2 kg is tied to one end of a 2 m long metal wire of $1.0 \mathrm{~mm}^2$ area of cross-section and rotated in a vertical circle such that the tension in the wire is zero at the highest point. If the maximum elongation in the wire is 2 mm , the Young's modulus of the metal is

(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

The ratio of the areas of cross-sections of three wires is $1: 2: 3$ and the ratio of the Young's modulii of their materials is $3: 2: 1$. If the three wires are of same length and same stretching force is applied to the three wires, then the ratio of the elongations of the three wires is

The dimensions of four wires of the same material are given below. The increase in length is maximum in the wire of

The length of four wires $A, B, C$ and $D$ made of same materials are $1 \mathrm{~m}, 2 \mathrm{~m}, 3 \mathrm{~m}$ and 4 m respectively. The radii of the wires $A, B, C$ and $D$ are $0.2 \mathrm{~mm}, 0.4 \mathrm{~mm}$, 0.6 mm and 0.8 mm respectively. For the same applied tension, the elongation is more in the wire

Two wires $A$ and $B$ of same length, same radius and same Young's modulus are heated to same range of temperatures. If the coefficient of linear expansion of $A$ is $\frac{3}{2}$ times that of $B$, then the ratio of the thermal stresses produced in the two wires $A$ and $B$ is

What is the work done in stretching a uniform metal wire of length from 2 m to 2.004 m with an area of cross-section $10^{-6} \mathrm{~m}^2$ ?

[Young's modulus of the wire $=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$ ]

One end of a steel rod of radius 10.0 mm and length 50.0 cm is clamped on a horizontal table. The other end of the rod is pulled with a force of magnitude 10.0 $\times \pi \mathrm{kN}$. This force is uniform across the flat surface of the rod and is perpendicular to it. The change in the length of the rod due to this applied force is (use Young's modulus, $Y=2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$ )

Two wires of same length having radius of 2 mm and 1.5 mm respectively, are loaded with same weights. Extension of the second wire is double than that of the first wire. What is the ratio of the Young's modulus of the first wire to that of the second wire?

An object of mass 15 kg is attached to the end of a metal wire of unstretched length 1.0 m . The object is then whirled in a vertical circle with an angular velocity of $4 \mathrm{rad} / \mathrm{s}$ at the bottom of the circle. If the cross sectional area of the wire is $0.05 \mathrm{~cm}^2$ and Young's modulus of metal is $2 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$, then the elongation of the wire when the mass is at the lowest point of its path (take, $g=10 \mathrm{~m} / \mathrm{s}^2$ )

A swimming pool has a depth of 22 m and area $700 \mathrm{~m}^2$. Calculate fractional change $\Delta v / v$ of water at the bottom of the swimming pool, given that the bulk modulus of water is $2.2 \times 10^9 \mathrm{Nm}^{-2}, g=10 \mathrm{~m} / \mathrm{s}^2$, and density of water is $1000 \mathrm{~kg} / \mathrm{m}^3$

$ \text { Match the following. } $

The correct match is

Young's modulus is proportionality constant that relates the force per unit area applied perpendicularly at the surface of an object to

Two metal wires $A$ and $B$ have length $L$ and $3 L$ respectively. The radius of cross-sectional circular area of wire $A$ and $B$ are $R$ and $2 R$, respectively. These wires are joined end to end along their axis. When one end of the combined system is fixed and other end is pulled with a constant force $F$, the elongation in both the wires is equal. If $Y_A$ and $Y_B$ are Young's modulus of wire $A$ and $B$, then the $Y_B / Y_A$ is

The length of a metal wire is found to be $L_1$ and $L_2$ when the tension of $T_1$ and $T_2$ are applied to it respectively. The natural length of the wire is

A slab of side 50 cm and thickness 10 cm is subjected to a shearing force of $10^5 \mathrm{~N}$ on its narrow edge. If the lower edge is riveted to the floor and upper edge is displaced by 0.2 mm , then shear modulus of the material of the slab is