When a metal wire is stretched by a load, the fractional change in its volume ΔV/V is proportional to

1. \(\frac{\Delta l}{l}\)

2. \(\left(\frac{\Delta l}{l}\right)^{2}\)

3. \(\sqrt{\Delta l/ l}\)

4. none of these

The length of a metal wire is l₁ when the tension in it is T₁ and is l₂ when the tension is T₂. The natural length of the wire is

1. \(\frac{l_{1}+l_{2}}{2}\)

2. \(\sqrt{l_{1} l_{2}}\)

3. \(\frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}}\)

4. \(\frac{l_{1} T_{2}+l_{2} T_{1}}{T_{2}+T_{1}}\)

A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break

1. when the mass is at the highest point

2. when the mass is at the lowest point

3. when the wire is horizontal

4. at an angle of cos^–1(1/3) from the upward vertical

When a metal wire elongates by hanging a load on it, the gravitational potential energy is decreased.

1. This energy completely appears as the increased kinetic energy of the block

2. This energy completely appears as the increased elastic potential energy of the wire

3. This energy completely appears as heat

4. None of these

The dimension ML^–1 T^–2 can correspond to

1. moment of a force    

2. surface tension

3. modulus of elasticity

4. coefficient of viscosity

A student plots a graph from his readings on the determination of Young modulus of a metal wire but forgets to put the labels (figure). The quantities on X and Y-axes may be respectively

(a) weight hung and length increased

(b) stress applied and length increased

(c) stress applied and strain developed

(d) length increased and the weight hung

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (a), (b) and (d)

4. All of these

A heavy uniform rod is hanging vertically from a fixed support. It is stretched by its own weight. The diameter of the rod is

1. smallest at the top and gradually increases down the rod

2. largest at the top and gradually decreases down the rod

3. uniform everywhere

4. maximum in the middle

A wire elongates by 1.0 mm when a load W is hang from it. If this wire goes over a pulley and two weights W each are hung at the two ends, the elongation of the wire will be

1. 0.5 m

2. 1.0 mm

3. 2.0 mm

4. 4.0 mm

Two wires A and B are made of same material. The wire A has a length I and diameter r while the wire B has a length 2l and diameter r/2. If the two wires are stretched by the same force, the elongation in A divided by the elongation in B is

1. 1/8

2. 1/4

3. 4

4. 8

A wire can sustain a weight of 20 kg before breaking. If the wire is cut into two equal parts, each part can sustain a weight of

1. 10 kg

2. 20 kg

3. 40 kg

4. 80 kg