A force applied on a brass wire of uniform cross-section area creates change in its length and cross-sectional area. If lateral strain produced in the wire is $3 \mathrm{x} {10}^{-2}$, then the energy stored per unit volume of wire will be: [${\mathrm{Y}}_{\mathrm{brass}} = 9 \mathrm{x} {10}^{10} \mathrm{N}/{\mathrm{m}}^2, {\mathrm{\sigma }}_{\mathrm{brass}} = 0.3$]

(1) 275 $\mathrm{MJ}/{\mathrm{m}}^3$

(2) 315 $\mathrm{MJ}/{\mathrm{m}}^3$

(3) 450 $\mathrm{MJ}/{\mathrm{m}}^3$

(4) 175 $\mathrm{GJ}/{\mathrm{m}}^3$

A uniform wire of length \(3\) m and mass \(10\) kg is suspended vertically from one end and loaded at another end by a block of mass \(10\) kg. The radius of the cross-section of the wire is \(0.1\) m. The stress in the middle of the wire is: (Take \(g=10\) ms^-2)

Three identical balls of rubber, aluminium, and steel are dropped from the same height on a horizontal rigid surface. If ${\mathrm{V}}_{\mathrm{rubber}} {\mathrm{V}}_{\mathrm{Al}}, \mathrm{and} {\mathrm{V}}_{\mathrm{steel}}$ are their speeds just after the collision, then

(1) ${\mathrm{V}}_{\mathrm{rubber}} = {\mathrm{V}}_{\mathrm{Al}} = {\mathrm{V}}_{\mathrm{steel}}$

(2) ${\mathrm{V}}_{\mathrm{rubber}} > {\mathrm{V}}_{\mathrm{Al}} > {\mathrm{V}}_{\mathrm{steel}}$

(3) ${\mathrm{V}}_{\mathrm{rubber}} < {\mathrm{V}}_{\mathrm{Al}} < {\mathrm{V}}_{\mathrm{steel}}$

(4) ${\mathrm{V}}_{\mathrm{rubber}} > {\mathrm{V}}_{\mathrm{Al}} = {\mathrm{V}}_{\mathrm{steel}}$

A solid cylinder of radius 10 cm and length 1 m clamped from its one end is twisted through an angle of 0.4 rad by applying torque at another free end. The shear strain developed in the cylinder will be:

(1) 0.2

(2) 0.8

(3) 0.02

(4) 0.04

If two wires of the same material and of the same length have a ratio of their radii 1:2, then under the effect of same stretching force their respective elongation will be in the ratio of:

(1) 1: 1

(2) 1: 2

(3) 4: 1

(4) 1: 4

The metal rod (Y = 2 x ${10}^{12}$ dyne/sq. cm) of the coefficient of linear expansion 1.6 x ${10}^{-5}$ per °C has its temperature raised by 20°C. The linear compressive stress to prevent the expansion of the rod is:

(1) 2.4 x ${10}^8$ dyne/sq. cm

(2) 3.2 x ${10}^8$ dyne/sq. cm

(3) 6.4 x ${10}^8$ dyne/sq. cm

(4) 1.6 x ${10}^8$ dyne/sq. cm

One end of a uniform wire of length L and weight ${\mathrm{W}}_0$, is attached rigidly to a point in the roof and weight ${\mathrm{W}}_1$ is suspended from its lower end. If S is the area of cross-section of the wire, the stress in the wire at a height L/4 from its lower end is:

(1) ${\mathrm{W}}_1$/S

(2) [${\mathrm{W}}_1$ + (${\mathrm{W}}_0$/4)]/S

(3) [${\mathrm{W}}_1$ + (3${\mathrm{W}}_0$/4)/S

(4) (${\mathrm{W}}_1$ + ${\mathrm{W}}_0$)/S

An elongation of 0.1% in a wire of cross-sectional area ${10}^{-6} {\mathrm{m}}^2$ causes tension of 100 N. The Young's modulus is:

(1) ${10}^{12}$ $\mathrm{N}/{\mathrm{m}}^2$

(2) ${10}^{11}$ $\mathrm{N}/{\mathrm{m}}^2$

(3) ${10}^{10}$ $\mathrm{N}/{\mathrm{m}}^2$

(4) ${10}^2$ $\mathrm{N}/{\mathrm{m}}^2$