The maximum load a wire can withstand without breaking when its length is reduced to half of its original length, will:

A spring is stretched by applying a load to its free end. The strain produced in the spring is:

A mild steel wire of length \(\mathrm{2L}\) and cross-sectional area \(A\) is stretched, well within the elastic limit, horizontally between two pillars (figure). A mass \(m\) is suspended from the mid-point of the wire. Strain in the wire is:

    
1. \( \frac{x^2}{2 L^2} \)
2. \(\frac{x}{\mathrm{~L}} \)
3. \(\frac{x^2}{L}\)
4. \(\frac{x^2}{2L}\)

A rectangular frame is to be suspended symmetrically by two strings of equal length on two supports (figure). It can be done in one of the following three ways;

The tension in the strings will be:

1. the same in all cases.

2. least in (a).

3. least in (b).

4. least in (c).

A wire is suspended from the ceiling and stretched under the action of a weight \(F\) suspended from its other end. The force exerted by the ceiling on it is equal and opposite to the weight.
 

The correct statements are:
1. (a), (b)
2. (a), (d)
3. (b), (c)
4. (a), (c)

A rod of length l and negligible mass is suspended at its two ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths (figure). The cross-sectional areas of wires A and B are $1.0 {\mathrm{mm}}^2 \mathrm{and} 2.0 {\mathrm{mm}}^2$ respectively. (${\mathrm{Y}}_{\mathrm{Al}}=70\times {10}^9 \mathrm{N}/{\mathrm{m}}^2 \mathrm{and} {\mathrm{Y}}_{\mathrm{steel}}=200\times {10}^9 \mathrm{N}/{\mathrm{m}}^2$)

The correct statements are:

1. (b, c)

2. (a, d)

3. (b, d)

4. (c, d)

A copper and a steel wire of the same diameter are connected end to end. A deforming force \(F\) is applied to this composite wire which causes a total elongation of \(1\) cm. The two wires will have:

Choose the correct option: