The breaking stress of a wire depends on:

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 light rod of length $2~\text{m}$ 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 $A_1 = 0.1~\text{cm}^2$ and brass wire of cross-sectional area $A_2 = 0.2~\text{cm}^2.$ To have equal stress in both wires, $\frac{T_1}{T_2}?$

lf $\rho$ 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. $\dfrac{2}{\rho g}$

2. $\dfrac{\rho}{\sigma g}$

3. $\dfrac{\rho g}{2 \sigma}$

4. $\dfrac{\sigma}{\rho g}$

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

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:

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 $W_1$ is suspended from its lower end. If $A$ is the area of the cross-section of the wire, the stress in the wire at a height $\frac{3L}{4}$ from its lower end is:
1. $\frac{W+W_1}{A}$
2. $\frac{4W+W_1}{3A}$
3. $\frac{3W+W_1}{4A}$
4. $\frac{\frac{3}{4}W+W_1}{A}$

A cube of aluminium of sides $0.1~\text{m}$ is subjected to a shearing force of $100$ N. The top face of the cube is displaced through $0.02$ cm with respect to the bottom face. The shearing strain would be:
1. $0.02$                                   
2. $0.1$
3. $0.005$                               
4. $0.002$

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)