The ratio of radii of two wires of the same material is 2: 1. If these wires are stretched by equal force, the ratio of stresses produced in them is:

1. 2: 1

2. 1: 2

3. 1: 4

4. 4: 1

A steel wire of diameter 2 mm has a breaking strength of $4\times {10}^5 \mathrm{N}$. What is the breaking force of similar steel wire of diameter 1.5 mm?

1. $2.3\times {10}^5 \mathrm{N}$

2. $2.6\times {10}^5 \mathrm{N}$

3. $3\times {10}^5 \mathrm{N}$

4. $1.5\times {10}^5 \mathrm{N}$

A steel wire is 1 m long and 1 mm² in area of cross section. If it takes 200 N to stretch this wire by 1 mm, how much force will be required to stretch a wire of the same material as well as diameter from its normal length of 10 m to a length of 1002 cm?

1. 1000 N

2. 200 N

3. 400 N

4. 2000 N

A rod of length l and radius r is held between two rigid walls so that it is not allowed to expand. If its temperature is increased, then the force developed in it is proportional to

1. l

2. $\frac{1}{\mathrm{l}}$

3. ${\mathrm{r}}^2$

4. ${\mathrm{r}}^{-2}$

A uniform cubical block is subjected to volumetric compression, which decreases its each side by 2%. The Bulk strain produced in it is

1. 0.03

2. 0.02

3. 0.06

4. 0.12

A material has Poisson's ratio 0.5. If a uniform rod of it suffers a longitudinal strain of $3\times {10}^{-3}$, what will be percentage increase in volume?

1. 2%

2. 3%

3. 5%

4. 0%

Hooke's law is applicable for:

When a load of 10 kg is suspended on a metallic wire, its length increase by 2mm. The force constant of the wire is

1. $3\times {10}^4 \mathrm{N}/\mathrm{m}$

2. $2.5\times {10}^3 \mathrm{N}/\mathrm{m}$

3. $5\times {10}^4 \mathrm{N}/\mathrm{m}$

4. $7.5\times {10}^3 \mathrm{N}/\mathrm{m}$

The figure shows the graph between stress and strain for a uniform wire at two different temperatures. Then:

1. \(T_1>T_2\)
2. \(T_2>T_1\)
3. \(T_1=T_2\)
4. None of these