Elasticity PYQs - Last 10 Years

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 $=2 \times 10^{11} \mathrm{Nm}^{-2}$ )

A steel rod with a circular cross-section of diameter 1 cm and another steel rod with a square cross-section of side 1 cm have equal mass. If the two rods are subjected to same tension, the ratio of the elongations of the two rods 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 s...

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

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 $=60 \mathrm{GPa}$ )

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 $...

A steel wire of length 3 m and a copper wire of length 2.2 m are connected end to end. When the combination is stretched by a force, the net elongation is 1.05 mm . If the area of cross-section of each wire is $6 \mathrm{~mm}^2$, then the l...

If the length of a string is $P$ when the tension in it is 6 N and its length is $Q$ when the original length of the string is

A simple pendulum is made of a metal wire of length $L$, area of cross-section $A$, material of Young's modulus $Y$ and a bob of mass $m$. This pendulum is hung in abus moving with a uniform speed $v$ on a horizontal circular road of radius...

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...

A wire of cross-sectional area $10^{-6} \mathrm{~m}^{2}$ is elongated by $0.1 \%$ when the tension in it is 1000 N . The Young's modulus of the material of the wire is (assume radius of the wire is constant)

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

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 t...

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 r...

A wire of length 40 cm is stretched by 0.1 cm . The strain on the wire is

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 pr...

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 r...

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 $=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$ ]

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...

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 ...

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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 \mathr...

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 com...

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

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

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 ...

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