Elasticity - Mechanics - Physics Previous Year Questions

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 $1000 \mathrm{~kg} / \mathrm{m}^3$

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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

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

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 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

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, $g=10 \mathrm{~m} / \mathrm{s}^2$ )

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, $Y=2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$ )

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

A steel rod has a radius of 10 mm and a length of 1 m . A 80 kN force stretches it along its length. If the Young's modulus of the rod is $2 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$, then the change in length is

If the bulk modulus of water is $2 \times 10^9 \mathrm{Nm}^{-2}$, then the required pressure to reduce the given volume of water by $2 \%$ is

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