If Poisson's ratio $\mathrm{\sigma }$ is $\frac{1}{2}$ for material, then the material is

(1) Incompressible

(2) Elastic fatigue

(3) Compressible

(4) Plastic

A wire can bear maximum force F. A wire of same material but triple radius can bear the maximum force of:

(1) F

(2) 3F

(3) 9F

(4) 27 F

The increase in the length of a wire on stretching is \(0.04\)%. If Poisson's ratio for the material of wire is \(0.5,\) then the diameter of the wire will:

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