Elasticity - Mechanics - Physics Previous Year Questions

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

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 $=60 \mathrm{GPa}$ )

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

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

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