A force \(F\) is needed to break a copper wire having radius \(R.\) The force needed to break a copper wire of radius \(2R\) will be:

A steel cable with a radius of 1.5 cm supports a chairlift at a ski area. If the maximum stress is not to exceed 10⁸ N/m², what is the maximum load that the cable can support?
1. 7.06 x 10⁴ N
2. 5.03 x 10⁴ N
3. 1.09 x 10⁴ N
4. 17 x 10⁴ N

The breaking stress of a wire going over a smooth pulley in the following question is 2 × ${10}^9$ N/${\mathrm{m}}^2$. What would be the minimum radius of the wire used if it is not to break?

A light rod of length 2m is suspended from the ceiling horizontally by means of two vertical wires of equal length. A weight W is hung from the light rod as shown in the figure. The rod is hung by means of a steel wire of cross-sectional area $A_1=0.1$ $c{m}^2$ and brass wire of cross-sectional area $A_2=0.2$ $c{m}^2$. To have equal stress in both wires, ${\mathrm{T}}_1/{\mathrm{T}}_2$=?

To break a wire, a force of ${10}^6$ $N/m^2$ is required. If the density of the material is $3\times {10}^3$ $kg/m^3$, then the length of the wire which will break by its own weight will be:

1. 34 m

2. 30 m

3. 300 m

4. 3 m

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)

lf $\mathrm{\rho }$ is the density of the material of a wire and $\sigma$ is the breaking stress, the greatest length of the wire that can hang freely without breaking is:

1.$\frac{2}{\mathrm{\rho g}}$

2. $\frac{\mathrm{\rho }}{\mathrm{\sigma g}}$

3.$\frac{\mathrm{\rho g}}{2\mathrm{\sigma }}$

4. $\frac{\mathrm{\sigma }}{\mathrm{\rho g}}$

The breaking stress of a wire depends on:

One end of a uniform wire of length L and of weight W is attached rigidly to a point in the roof and a weight W₁ is suspended from its lower end. If A is the area of cross-section of the wire , the stress in the wire at a height 3L/4 from its lower end is:

1.  $\frac{\mathrm{W}+{\mathrm{W}}_1}{\mathrm{A}}$

2.  $\frac{4\mathrm{W}+{\mathrm{W}}_1}{3\mathrm{A}}$

3.  $\frac{3\mathrm{W}+{\mathrm{W}}_1}{4\mathrm{A}}$

4.  $\frac{{\displaystyle \frac{3}{4}}\mathrm{W}+{\mathrm{W}}_1}{\mathrm{A}}$

A wire can sustain a weight of 10 kg before breaking. If the wire is cut into two equal parts, then each part can sustain a weight of: