Mechanical Properties of Solids

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by Δl on applying a force F, how much force is needed to stretch the second wire by the same amount?

• 9F

• 6F

• F

• 4F

The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is

• 13.2 cm

• 8 cm

• 16 cm

• 12.5 cm

A ball falling in a lake depth 200 m shows a decrease of 0.1 % in its volume at the bottom then the bulk modulus of the material of the ball is

• $19.6\times {10}^8 \mathrm{N}/{\mathrm{m}}^2$

• $19.2\times {10}^7\mathrm{N}/{\mathrm{m}}^2$

• $24\times {10}^9 \mathrm{N}/{\mathrm{m}}^2$

• $24\times {10}^5 \mathrm{N}/{\mathrm{m}}^2$

A fixed volume of iron is drawn into a wire of length l. The extension x produced in this wire by a constant force F is proportional to

• l

• $\frac{1}{\mathrm{l}}$

• ${\mathrm{l}}^2$

• $\frac{1}{{\mathrm{l}}^2}$

Two bars A and B of circular cross-section and same volume made of same material are subjected under same tension. If the diameter of A is half that of B. The ratio of extension of A to B will be

• 16

• 2

• $\frac{1}{4}$

• 4

The dimensional formula for Young's modulus is

• $\left[\mathrm{M} {\mathrm{L}}^{-1} {\mathrm{T}}^{-2}\right]$

• $\left[{\mathrm{M}}^{\mathrm{o}} \mathrm{L} {\mathrm{T}}^{-2}\right]$

• $\left[\mathrm{M} \mathrm{L} {\mathrm{T}}^{-2}\right]$

• $\left[\mathrm{M} {\mathrm{L}}^2{\mathrm{T}}^{-2}\right]$

The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young's double slit experiment is

• infinite

• five

• three

• zero

A wire can be broken by applying load of 200 N. The force required to break another wire of the same length and same material, but double in diameter is

• 200 N

• 400 N

• 600 N

• 800 N

A cube of side 40 mm has its upper face displaced by 0.1 mm by a tangential force of 8 kN. The shearing modulus of cube is

• 2 × 10⁹ Nm^-2

• 4 × 10⁹ Nm^-2 

• 8 × 10⁹ Nm^-2

• 16 × 10⁹ Nm^-2

If Young's double slit experiment is performed i water instead of air, then

• no fringes would be seen

• fringe width would decrease

• fringe width would increase

• fringe width would remain unchanged