Mechanical Properties of Solids

A wire is suspended from the ceiling and stretched under the action of a weight F suspended from its other end. The force exerted by the ceiling on it is equal and opposite to the weight.

(a) Tensile stress at any cross section A of the wire is F/A

(b) Tensile stress at any cross section is zero

(c) Tensile stress at any cross section A of the wire is 2F/A

(d) Tension at any cross section A of the wire is F

The stress-strain graphs for two materials are shown in Fig.9.3 (assume same scale).

(a) Material (ii) is more elastic than material (i) and hence material (ii) is more brittle.

(b) Material (i) and (ii) have the same elasticity and the same brittleness.

(c) Material (ii) is elastic over a larger region of strain as compared to (i).

(d) Material (ii) is more brittle than material (i).

A rectangular frame is to be suspended symmetrically by two strings of equal length on two supports (Fig. 9.2). It can be done in one of the following three ways The tension in the strings will be

(a) The same in all cases

(b) Least in (a)

(c) Least in (b)

(d) Least in (c)

A mild steel wire of length 2L and cross-sectional area A is stretched, well within elastic limit, horizontally between two pillars (Fig. 9.1). A mass m is suspended from the midpoint of the wire. Strain in the wire is

(a)  

(b) x/L

(c) x²/2L

(d)  

A rigid bar of mass M is supported symmetrically by three wires each of length l . Those at each end are of copper and the middle one is of iron. The ratio of their diameters, if each is to have the same tension, is equal to

(a) Y_copper /Y_iron

(b) $\sqrt[]{\frac{{\mathit{Y}}_{\mathit{i}\mathit{r}\mathit{o}\mathit{n}}}{{\mathit{Y}}_{\mathit{c}\mathit{o}\mathit{p}\mathit{p}\mathit{e}\mathit{r}}}}$  

(c) $\frac{{\mathit{Y}}_{\mathit{i}\mathit{r}\mathit{o}\mathit{n}}^2}{{\mathit{Y}}_{\mathit{c}\mathit{o}\mathit{p}\mathit{p}\mathit{e}\mathit{r}}^2}$

(d)  Y_iron/Y_copper .

A spring is stretched by applying a load to its free end. The strain produced in the spring is

(a) Volumetric

(b) Shear

(c) Longitudinal and shear

(d) Longitudinal

The temperature of a wire is doubled. The Young's modulus of elasticity

(a) Will also double

(b) Will become four times

(c) Will remain same

(d) Will decrease

The maximum load a wire can withstand without breaking, when its length is reduced to half of its original length, will

(a) Be double

(b) Be half

(c) Be four times

(d) Remain same

Modulus of rigidity of ideal liquids is

(a) Infinity

(b) Zero

(c) Unity

(d) Some finite small non-zero constant value