Question 4 : State whether true or false :<br>The hollow shaft is much stronger than a solid shaft of same mass, same length and same material.

Question 5 : Assertion: The strain present in the material after unloading is called the residual strain or plastic strain and the strain disappears during unloading is termed as recoverable or elastic strain. Reason: After yieild point, there is some residual stress left in an material on unloading.

Question 6 : The property of a material due to which shape is changed permanently is known as:<br/>

Question 7 : A wire whose cross-sectional area is $4\ mm^{2}$ is stretched by $0.1\ mm$ by a certain load. If a similar wire of double the area of cross-section is under the same load, then the elongation would be

Question 8 : The force required to double the length of the steel wire of area of cross section $5\times 10^{-5}m^{2}\quad (Y=20\times 10^{10}Pa)$ in $N$ is:

Question 9 : A wire is stretched to double its length. The strain is :

Question 10 : Assertion (A): Steel is more elastic than rubber.<br/>Reason (R) : Under a given deforming force, steel&#160;is deformed less than rubber.<br/>A) Both Assertion and Reason are true and the&#160;reason is correct explanation of the assertion<br/>B)Both Assertion and Reason are true, but reason&#160;is not correct explanation of the assertion<br/>C) Assertion is true, but the reason is false<br/>D) Assertion is false, but the reason is true

Question 11 : A fractional change in volume of oil is $1$ percent when a pressure of $2\times 10{7}Nm^{-2}$ is applied calculate the bulk modulus and its compressibility :

Question 12 : The length of an iron wire is $L$ and area of cross-section is $A$. The increase in length is $l$ on applying the force $F$ on its two ends. Which of the statement is correct?

Question 13 : A wire is stretched 1 mm by a force of 1 kN. How far would a wire of the same material and length but of four times that diameter he stretched by the same force?

Question 14 : A wire suspended vertically is stretched by a $20\ kgf$. Applied to its free end. The increase in length of the wire is $2\ mm$. The energy stored in the wire is $\left (g=10\ ms^{-2}\right)$:

Question 15 : Which apparatus are used to measure Y of a wire and shear modulus of the wire?<br>

Question 16 : The bulk modulus of water is $2.0\times { 10 }^{ 9 }\ { N }/{ { m }^{ 2 } }$ . The pressure required to increase the density of water $0.1 \%$ is

Question 17 : Two wires of the same material and length are stretched by the same force. Their masses are in the ratio $3 : 2$. Their elongations are in the ratio<br>

Question 18 : For a constant hydraulic stress on an object, the fractional change in the object's volume ($\displaystyle \Delta { V }/{ V }$) and its bulk modulus (B) are related as:

Question 20 : The elongation produced in a copper wire of length 2m and diameter 3mm, when a force of 30N is applied is [Y$=$1x10$^{11}$N.m$^{-2}$]

Question 21 : A wire elongates by $1 mm$ when a load W is hanged from it. lf the wire goes over a pulley and two weights $\mathrm{W}$ each are hung at the two ends, the elongation of the wire will be (in mm):<br/>

Question 22 : The stress along the length of a rod(with rectangular cross section) is $1\%$ of the Young's modulus of its material. What is the approximate percentage of change of its volume? (Poisson's ratio of the material of the rod is $0.3$).

Question 23 : Two wire A and B have equal lengths and are made of the same material, but the diameter of A is twice that of wire B. Then, for given load<br>

Question 24 : Temperature of a gas is $20^{0}\mathrm{C}$ and pressure is changed from $1.01\times 10^{5}$ Pa to $1.165\times 10^5\mathrm{P}\mathrm{a}$. If volume is decreased isothermally by 10%. The bulk modulus of gas is (in $Pa$):<br/><br/>

Question 25 : Two metal wire 'P' and 'Q' of same length and material are stretched by same load. Their masses are in the ratio $m_1 : m_2$. The ratio of elongations of wire 'P' to that of 'Q' is

Question 26 : Take, bulk modulus of water $B = 2100\ MPa$.<br/>What increase in pressure is required to decrease the volume of $200\ litres$ of water by $0.004$ percent?

Question 27 : Two rods of different materials having coefficients of thermal expansion and Young's moduli ${Y}_{1}, {Y}_{2}$, respectively are fixed between two rigid massive walls. The rods are heated such that undergo the same increase in temperature. There is no bending of the rods. If ${\alpha}_{1}:{\alpha}_{2}= 2:3$, the thermal stresses developed in the two rods are equal provided ${Y}_{1}: {Y}_{2}$ is equal to:<br/>

Question 28 : The density of water at the surface of the ocean is $\rho$ and atmospheric pressure is ${P}_{0}$. If the bulk modulus of water is $K$, what is the density of ocean water at a depth where the pressure is then$n{P}_{0}$?

Question 29 : An increase in pressure required to decreases the $200$ litres volume of a liquid by $0.004\%$ in the container is(Bulk modulus of the liquid $=2100$ MPa).

Question 30 : A solid sphere of radius $R$ and density $\rho $ is attached to one end of a mass-less spring of force constant $k$. The other end of the spring is connected to another solid sphere of radius $R$ and density $3\rho $. The complete arrangement is placed in a liquid of density $2\rho $ and is allowed to reach equilibrium. The correct statement(s) is (are)<br>