Two wires of the same material have lengths in the ratio of 1: 2. If they are stretched by applying equal forces, the increase in lengths is the same. The ratio of their respective radii is:

(1) 1: 1

(2) 1: 2

(3) 1: $\sqrt{2}$

(4) 2: 1

The value of Poisson's ratio cannot be:

(1) 0.05

(2) 0.32

(3) 0.63

(4) 0.49

A steel wire of cross-sectional area 3 x ${10}^{-6} {\mathrm{m}}^2$ can withstand a maximum strain of ${10}^{-3}$. If Young's modulus of steel is 2 x ${10}^{11} {\mathrm{Nm}}^{-2}$, then maximum mass which the wire can hold is: (Take g =10 $\mathrm{m}/{\mathrm{s}}^2$)

(1) 40 kg

(2) 100 kg

(3) 80 kg

(4) 60 kg

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)