Mechanical properties of solids practice · Medium

A rod elongated by $l$ when a body of mass $M$ is suspended from it. The work done is

A copper wire of negligible mass, $\mathrm{1 m}$ length and cross-sectional area ${10^{ - 6}}$ is kept on a smooth horizontal table with one end fixed. A ball of mass $\mathrm{1}$ kg is attached to the other end. The wire and the ball are rotated with an angular velocity 20 rad ${s^{ - 1}}$. If the elongation in the wire is ${10^{ - 3}}\mathrm{m}$, then the Young’s modulus is

The pressure on an object of bulk modulus B undergoing hydraulic compression due to a stress exerted by surrounding fluid having volume strain $\left(\frac{\Delta V}{V}\right)^2$ is

The maximum elongation of a steel wire of $1 \mathrm{~m}$ length if the elastic limit of steel and its Young's modulus, respectively, are $8 \times 10^8 \mathrm{~N} \mathrm{~m}^{-2}$ and $2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2},$ is:

Assertion: The force exerted by a spring is directly proportional to its displacement from its equilibrium position.

Reason: The spring force follows Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement from its equilibrium position.

Two rods of copper and steel having same area of cross - section but different lengths $l_{1}$ and $l_{2}$ respectively are connected to each other. The combined length of two rods fits between two walls without any stress on walls. If $\alpha_{1}$ and $\alpha_{2}$ are their coefficient of linear expansion, $Y_{1}$ and $Y_{2}$ are their Young's modulus respectively, then (There is no buckling of rods while heating) With increase in temperature:

Statement-I: If the volume of a body remains unchanged, When subjected to tensile strain, the value of Poisson's ratio is $1 / 2$
Statement-II: Phosphor bronze has low Young's modulus and high rigidity modulus

The approximate depth of an ocean is $3000 \mathrm{~m}$. The compressibility of water is $5 \times 10^{-10} \mathrm{~Pa}^{-1}$ and density of water is $10^3 \mathrm{~kg} / \mathrm{m}^3$. What fractional compression of water will be obtained at the bottom of the ocean.

A steel rod $y = 2 \times {10^{11}}\,N/{m^2}$ and $\alpha = {10^{ - 5}}/\,{\,^ \circ }C$ of length 1m and area of cross section $1\,c{m^2}$ is heated from ${0^ \circ }C$ to ${200^ \circ }C$ with out being allowed to extend or bend. What is the tension produced in the rod?

Energy stored in stretching a string per unit volume is

Stress to strain ratio is equivalent to

When a spiral spring is stretched by force, strain produced is

Two wires of same material and length but radii in the ratio 1 : 4 are stretched by two forces to produce equal elongation. The ratio of two forces is

Statement I: Glassy solids have sharp melting point.
Statement II: The bonds between the atoms of glassy solids broken at the same temperature.

The volume of a solid at 1 atmosphere pressure is $10^4 \mathrm{~cm}^3$. If the pressure is increased to 51 atmosphere then percentage change in its volume will be $\left(\mathrm{K}=10^{12}\right.$ dyne/ $\left.\mathrm{cm}^2\right)$-

In above question, the work done in the two wires is

Statement I: Stress is the internal force per unit area of the body.
Statement II: Rubber is more elastic than steel.

Assertion: A material which stretches more is more elastic.
Reason: Rubber is more elastic than steel.

The specific heat at constant pressure and at constant volume for an ideal gas are ${C_p}$ and ${C_v}$ and its adiabatic and isothermal elasticities are ${E_\phi }$ and ${E_\theta }$ respectively. The ratio of ${E_\phi }$ to ${E_\theta }$ is

Assertion: Two wires $A$ and $B$ have the same cross-sectional area and are made of the same material but the length of wire $A$ is twice that of $B$. For a given load, the strain in wire $A$ is twice that in $B$.
Reason: For a given load, the extension in a wire is not proportional to its length.

In magnitude hydraulic stress is equal to:

The Marina trench is located in the Pacific Ocean and at one place it is nearly eleven $\mathrm{km}$ beneath the surface of water. The water pressure at the bottom of the trench is about $1.1 \times 10^8 \mathrm{~Pa}$. A steel ball of initial volume $0.32 \mathrm{~m}^3$ is dropped into the ocean and falls to the bottom of the trench. What is the change in the volume of the ball when it reaches to the bottom?

Assertion(A): Upto the elastic limit, strain $\propto$ stress.

Reason(R): Upto elastic limit, material returns to its original shape and size, when external force is removed.

Assertion:- Elastic restoring forces may be conservative
Reason:- The value of strain for same stress are different while increasing the load and while decreasing the load.

The area of cross section of a steel wire $\left( {Y = 2.0\,\, \times {{10}^{11}}\,N/{m^2}} \right)$ is $0.1\,\,c{m^2}$. The force required to double its length will be

Consider the two statements.

I. Mach number is the ratio of strain to stress.

II. Sound waves in air are longitudinal while light waves in air are transverse.

Choose the correct option among the following.

When a spring is stretched by a distance $x$ , it exerts a force given by $F = \left[ { - 5x - 16{x^3}} \right]N$.
The work done, when the spring is stretched from $0.1\,\,m\,\,\mathrm{to}\,\,0.2\,\,m$ is

Statement I: Strain is a unitless quantity.
Statement II: Strain is equivalent to force.

Which of the following statements is correct?

If the area of cross-section is halved and length of wire having young's modulus $Y$ is doubled, then its young's modulus will become