Mechanical Properties of Solids

A wire canbe brokenbyapplyinga load of200 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  tangenbtial force of 8 kN. The shearing modulus of cube is

• 2 × 10⁹ Nm^-2

• 4 $$\begin{gathered} \mathrm{Shearing} \mathrm{modulus} \mathrm{of} \mathrm{cube} \\ \mathrm{\eta } = \frac{\mathrm{Fl}}{\mathrm{A}∆\mathrm{l}} = \frac{8 \times {10}^3 \times 40 \times {10}^{-3}}{{\left(40 \times {10}^{-3}\right)}^2 \times \left(0.1 \times {10}^{-3}\right)} \\ = 2 \times {10}^{9 } {\mathrm{Nm}}^{-2} \end{gathered}$$ Nm^-2

• 8 × 10⁹ Nm^-2

• 16 × 10⁹ Nm^-2

A wire of length L and area of cross-section A is stretched through a distance x metre by applying a force F along length, then the work done in this process is (Y is Young's modulus of the material)

• $\frac{1}{2} \left(\mathrm{A} . \mathrm{L}\right) \left(\frac{\mathrm{Yx}}{\mathrm{L}}\right) \left(\frac{\mathrm{x}}{\mathrm{L}}\right)$

• $\left(\mathrm{A} .\hspace{0.17em}\mathrm{L}\right) \left(\mathrm{YL}\right) \left(\frac{\mathrm{x}}{\mathrm{L}}\right)$

• $2\left(\mathrm{A} . \mathrm{L}\right) \left(\mathrm{YL}\right) \left(\frac{\mathrm{x}}{\mathrm{L}}\right)$

• $3 \left(\mathrm{A} . \mathrm{L}\right) \left(\mathrm{YL}\right) \left(\frac{\mathrm{x}}{\mathrm{L}}\right)$

The modulus of elasticity is dimensionally equivalent to

• strain

• force

• stress

• coefficient of viscosity

Which of the following substance has the highest elasticity ?

• Steel

• Copper

• Rubber

• Sponge

The Poisson's ratio of a material is 0.5. If a force is applied to a wire of this material, there is a decrease in the cross-sectional area by 4%. The percentage increase in the length is

• 1 %

• 2 %

• 2.5 %

• 4 %

A material has Poisson's ratio 0.50. If a uniform rod of it suffers a longitudinal strain of 2 x 10^-3 , then the percentage change in volume is

• 0.6

• 0.4

• 0.2

• zero

Let L be the length and d be the diameter of cross- section of a wire. Wires of the same material with different L and d are subjected to the same tension along the length of the wire. In which of the following cases, the extension of wire will be the maximum ?

• L = 200 cm, d = 0.5 mm

• L = 300 cm, d = 1.0 mm

• L = 50 cm, d = 0.05 mm

• L = 100 cm, d = 0.2 mm

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied ?

• Length = 50 cm, diameter = 0.5 mm

• Length = 100 cm, diameter = 1 mm

• Length = 200 cm, diameter = 2 mm

• Length= 300 cm, diameter= 3 mm

A metal rod is fixed rigidly at two ends so as to prevent its thermal expansion. If L, α and Y respectively denote the length of the rod, coefficient of linear thermal expansion and Young's modulus of its material, then for an increase in temperature of the rod by ΔT, the longitudinal stress developed in the rod is

• inversely proportional to α

• inversely proportional to Y

• directly proportional to ΔT/Y

• independent of L