Mechanical Properties of Solids

Choose the wrong statement

• The bulk modulus for solids is much larger than for liquids

• Gases are least compressible

• The incompressibility of the solids is due to the tight coupling between neighbouring atoms

• The reciprocal of the bulk modulus is called compressibility

Identify the incorrect statement.

• Young's modulus and shear modulus are relevant only for solids.

• Bulk modulus is relevant for solids, liquids and gases.

• Alloys have larger values of Young's modulus than metals.

• Metals have larger values of Young's modulus than elastomers

A lead bullet strikes against a steel plate with a velocity 200 ms^-1. If the impact is perfectly inelastic and the heat produced is equally shared between the bullet and the target, then the rise in temperature of the bullet is (Specific heat capacity of lead = 125 J Kg^-1 K^-1)

• 80°C

• 60°C

• 160°C

• 40°C

Which one of the following statements is correct? In the case of

• shearing stress there is change in volume

• tensile stress there is no change in volume

• shearing stress there is no change in shape

• hydraulic stress there is no change in volume

The Young's modulus of the material of a wire is 2 × 10¹⁰ Nm^-2. If the elongation strain is 1 %, then the energy stored in the wire per unit volume in Jm^-3 is

• 10⁶

• 10⁸

• 2 × 10⁶

• 2 × 10⁸

If the volume of a block of aluminium is decreased by 1%, the pressure (stress) on its surface is increased by (Bulk modulus of Al = 7.5 10¹⁰ Nm^-2)

• 7.5 × 10¹⁰ Nm^-2

• 7.5 × 10⁸ Nm^-2

• 7.5 × 10⁶ Nm^-2

• 7.5 × 10⁴ Nm^-2

The length of a rubber cord is 11 metre when the tension is 4 N and l₂ metre when the tension is 6 N. The length when the tension is 9 N, is

• (2.5 l₂ − 1.5 l₁) m

• (6 l₂ − 1.5 l₁) m

• (3 l₂ − 2 l₁) m

• (3.5 l₂ − 2.5 l₁) m

A wire of natural length l, Young's modulus Y and area of cross-section A is extended by x. Then the energy stored in the wire is given by

• $\frac{1}{2} \frac{\mathrm{YA}}{\mathrm{l}} {\mathrm{x}}^2$

• $\frac{1}{3} \frac{\mathrm{YA}}{\mathrm{l}} {\mathrm{x}}^2$

• $\frac{1}{2} \frac{\mathrm{Yl}}{\mathrm{A}} {\mathrm{x}}^2$

• $\frac{1}{2} \frac{\mathrm{YA}}{{\mathrm{l}}^2} {\mathrm{x}}^2$

A piece of solid weighs 120 g in air, 80 g in water and 60 g in a liquid. The relative density of the solid and that of the liquid are respectively

• 3, 2

• $2, \frac{3}{4}$

• $3, \frac{3}{2}$

• 4, 3

A work of 2 x 10^-2 J is done on a wire of length 50 cm and area of cross-section 0.5 mm². If the Young's modulus of the matenal of the wire is 2 × 10¹⁰ Nm^-2, then the wire must be

• elongated to 50.1414 cm

• contracted by 2.0 mm

• stretched by 0.707 mm

• of length changed to 49.293 cm