A rope 1 cm in diameter breaks if the tension in it exceeds 500 N. The maximum tension that may be given to a similar rope of diameter 2 cm is

1. 500 N

2. 250 N

3. 1000 N

4. 2000 N

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 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

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

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