The length of wire, when M₁ is hung from it, is l₁ and is l₂ with both M₁ and M₂ hanging. The natural length of wire is

1. $\frac{{\mathrm{M}}_1}{{\mathrm{M}}_2}({\mathrm{l}}_1-{\mathrm{l}}_2)+{\mathrm{l}}_1$

2. $\frac{{\mathrm{M}}_2{\mathrm{l}}_1-{\mathrm{M}}_1{\mathrm{l}}_2}{{\mathrm{M}}_1+{\mathrm{M}}_2}$

3. $\frac{{\mathrm{l}}_1+{\mathrm{l}}_2}{2}$

4. $\sqrt{{\mathrm{l}}_1{\mathrm{l}}_2}$

The substances having very short plastic region are

1. Ductile

2. Brittle

3. Malleable

4. All of these

Due to the addition of impurities, the modulus of elasticity:

1. Decreases

2. Increases

3. Remains constant

4. May increase or decrease

A load of 2 kg produces an extension of 1 mm in a wire of 3 m in length and 1 mm in diameter. The Young's Modulus of wire will be

1. $3.25\times {10}^{10} {\mathrm{Nm}}^{-2}$

2. $7.48\times {10}^{12} {\mathrm{Nm}}^2$

3. $7.48\times {10}^{10} {\mathrm{Nm}}^{-2}$

4. $7.48\times {10}^{-10} {\mathrm{Nm}}^{-2}$

The value of Young's Modulus for a perfectly rigid body is

1. 1 

2. Less than 1

3. Zero

4. Infinite

A spherical ball contracts in a volume by 0.01% when subjected to a normal uniform pressure of 100 atm. The Bulk modulus of its material is

1. $1.01\times {10}^{11} {\mathrm{Nm}}^2$

2. $1.01\times {10}^{12} {\mathrm{Nm}}^{-2}$

3. $1.01\times {10}^{10} {\mathrm{Nm}}^{-2}$

4. $1.01\times {10}^{13} {\mathrm{Nm}}^{-2}$

A metallic rod of length l and cross-sectional area A is made of a material of Young's Modulus Y. If the rod is elongated by an amount y, then the work done is proportional to

1. y

2. $\frac{1}{\mathrm{y}}$

3. ${\mathrm{y}}^2$

4. $\frac{1}{{\mathrm{y}}^2}$

If the Bulk Modulus of lead is $8.0\times {10}^9 \mathrm{N}/{\mathrm{m}}^2$ and the initial density of the lead is 11.4 g/cc, then under the pressure of $2.0\times {10}^8 \mathrm{N}/{\mathrm{m}}^2$, the density of the lead is

1. 11.3 g/cc

2. 11.5 g/cc

3. 11.6 g/cc

4. 11.7 g/cc

For a given material, the Young's Modulus is 2.4 times its modulus of rigidity. Its Poisson's ratio is

1. 0.2

2. 0.4

3. 1.2

4. 2.4

When the temperature of a gas is constant at $20°\mathrm{C}$ and pressure is changed from ${\mathrm{P}}_1=1.01\times {10}^5 \mathrm{Pa}$ to ${\mathrm{P}}_2=1.165\times {10}^5 \mathrm{Pa}$, then the volume changes by 10%. The Bulk modulus of the gas is

1. $1.55\times {10}^5 \mathrm{Pa}$

2. $1.01\times {10}^5 \mathrm{Pa}$

3. $1.4\times {10}^5 \mathrm{Pa}$

4. $0.115\times {10}^5 \mathrm{Pa}$