A man grows into a giant such that his linear dimensions increase by a factor of \(9.\) Assuming that his density remains the same, the stress in the leg will change by a factor of:
1. \(9\)

2. \(\dfrac{1}{9}\)

3. \(81\)

4. \(\dfrac{1}{81}\)

In an experiment, brass and steel wires of length \(1~\text{m}\) each with areas of cross section \(1~\text{mm}^2\) are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of \(0.2~\text{mm}\) is, [Given, the Young's Modulus for steel and brass are, respectively, \(120 \times 10^9 ~\text{N/m}^2\) and \(60 \times 10^9 ~\text{N/m}^2\)]
1. \( 4.0 \times 10^6 ~\text{N/m}^2\)
2. \( 1.2 \times 10^6~\text{N/m}^2\)
3. \( 1.8 \times 10^6~\text{N/m}^2\)
4. \(8 \times 10^6~\text{N/m}^2\)

The elastic limit of brass is 400 MPa. What should be the minimum diameter of a brass rod if it is to support a 400\(\pi \) N load without exceeding its elastic limit?
1. 1 mm
2. 1.5 mm
3. 2 mm
4. 2.5 mm

A uniform metallic wire is elongated by \(0.04\) m when subjected to a linear force \(F\). The elongation, if its length and diameter are doubled and subjected to the same force will be: