The modulus of rigidity of the ideal liquid is:

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

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

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

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:

1. ${\mathrm{Y}}_{\mathrm{Copper}}/{\mathrm{Y}}_{\mathrm{iron}}$

2. $\sqrt{\frac{{\mathrm{Y}}_{\mathrm{iron}}}{{\mathrm{Y}}_{\mathrm{Coper}}}}$

3. $\frac{{{\mathrm{Y}}^2}_{\mathrm{iron}}}{{{\mathrm{Y}}^2}_{\mathrm{copper}}}$

4. $\frac{{\mathrm{Y}}_{\mathrm{iron}}}{{\mathrm{Y}}_{\mathrm{Copper}}}$

A mild steel wire of length \(\mathrm{2L}\) and cross-sectional area \(A\) is stretched, well within the elastic limit, horizontally between two pillars (figure). A mass \(m\) is suspended from the mid-point of the wire. Strain in the wire is:

    
1. \( \frac{x^2}{2 L^2} \)
2. \(\frac{x}{\mathrm{~L}} \)
3. \(\frac{x^2}{L}\)
4. \(\frac{x^2}{2L}\)

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

The tension in the strings will be:

1. the same in all cases.

2. least in (a).

3. least in (b).

4. least in (c).

Consider two cylindrical rods of identical dimensions, one of rubber and the other of steel. Both the rods are fixed rigidly at one end of the roof. A mass M is attached to each of the free ends at the centre of the rods.
 

The stress-strain graphs for the two materials are shown in the figure. (assumed same scale)

The correct statements are:

1. (a, c)
2. (c, d)
3. (b, c)
4. (b, d)

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.
 

The correct statements are:
1. (a), (b)
2. (a), (d)
3. (b), (c)
4. (a), (c)