A uniform wire of cross-sectional area A is stretched by a certain force so that its length is elongated by x. What should be the cross-sectional area of the wire, so that elongation becomes $\frac{\mathrm{x}}{2}$ on applying the same force?

(1) A

(2) 2A

(3) 4A

(4) 8A

A wire suspended vertically from one of its ends is stretched by attaching a weight of 100 N. If the elastic energy stored in the wire is 0.1 J. The elongation in the wire is:

(1) 1 mm

(2) 2 mm

(3) 3 mm

(4) 4 mm

If E is the energy stored per unit volume in a wire having Young's modulus of the material Y, then stress applied is:

1.  $\sqrt{2\mathrm{EY}}$

2.  $2\sqrt{\mathrm{EY}}$

3.  $\frac{1}{2}\sqrt{\mathrm{EY}}$

4.  $\frac{3}{2}\sqrt{\mathrm{EY}}$

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: