Mechanical Properties of Solids

In plotting stress versus strain curves for two materials $P$ and $Q$, a student by mistake puts strain on the $y$-axis and stress on the $x$-axis as shown in the figure. Then the correct statement(s) is(are)

A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to $T_M$. If the Young's modulus of the material of the wire is Y then $\dfrac1Y$ is equal to :

(g = gravitational acceleration)

The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by 100°C is :

(For steel Young's modulus is $2\times10^{11}$ N m$^{-2}$ and coefficient of thermal expansion is $1.1\times10^{-5}$ K$^{-1}$)

In materials like aluminium and copper, the correct order of magnitude of various elastic modulii is :

The Bulk moduli of Ethanol, Mercury and water are given as 0.9, 25 and 2.2 respectively in units of $10^9$ Nm$^{-2}$. For a given value of pressure, the fractional compression in volume is $\dfrac{\Delta V}V$. Which of the following statements about $\dfrac{\Delta V}V$ for these three liquids is correct ?

Steel ruptures when a shear of $3.5\times10^8$ N m$^{-2}$ is applied. The force needed to punch a 1 cm diameter hole in a steel sheet 0.3 cm thick is nearly :

One end of a horizontal thick copper wire of length $2L$ and radius $2R$ is welded to an end of another horizontal thin copper wire of length $L$ and radius $R$. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is

A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in radian/s) is

Steel wire of length 'L' at 40 °C is suspended from the ceiling and then a mass 'm' is hung from its free end. The wire is cooled down from 40 °C to 30 °C to regain its original length 'L'. The coefficient of linear thermal expansion of the steel is $10^{-5}$/°C, Young's modulus of steel is $10^{11}\ \mathrm{N/m^2}$ and radius of the wire is 1 mm. Assume that L >> diameter of the wire. Then the value of 'm' in kg is nearly

A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1m and its cross-sectional area is $4.9\times10^{-7}\ \mathrm m^2$. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad s⁻¹. If the Young's modulus of the material of the wire is $n\times10^9$ N m⁻², the value of n is