Advertisements
Advertisements
Question
When a metal wire is stretched by a load, the fractional change in its volume ∆V/V is proportional to
Options
\[\frac{∆ \text{l}}{\text{ l }}\]
\[\left( \frac{∆ \text{ l }}{\text{ l }} \right)^2\]
\[\sqrt{∆ \text{ l / l}}\]
none of these
Advertisements
Solution
\[\frac{∆ \text{l}}{\text{ l }}\]
\[\text{ C . S . A . = A }\]
\[\text{ Length = l}\]
\[\text{ Volume of the wire V = Al }\]
\[\text{ Assuming no lateral strain when longitudinal strain occurs: }\]
\[\text{ Increase in volume: ∆ V = A ∆ l }\]
\[ \Rightarrow \frac{∆ V}{V} = \frac{A ∆ \text{ l }}{\text{ Al }} = \frac{∆ \text{ l }}{\text{ l }}\]
\[\text{ So,} \frac{∆ V}{V} \text{ is directly proportional to } \frac{∆ \text{l}}{\text{ l }}\] .
APPEARS IN
RELATED QUESTIONS
A rigid bar of mass 15 kg is supported symmetrically by three wires each 2.0 m long. Those at each end are of copper and the middle one is of iron. Determine the ratio of their diameters if each is to have the same tension.
Two strips of metal are riveted together at their ends by four rivets, each of diameter 6.0 mm. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed 6.9 × 107 Pa? Assume that each rivet is to carry one-quarter of the load.
When the skeleton of an elephant and the skeleton of a mouse are prepared in the same size, the bones of the elephant are shown thicker than those of the mouse. Explain why the bones of an elephant are thicker than proportionate. The bones are expected to withstand the stress due to the weight of the animal.
The yield point of a typical solid is about 1%. Suppose you are lying horizontally and two persons are pulling your hands and two persons are pulling your legs along your own length. How much will be the increase in your length if the strain is 1% ? Do you think your yield point is 1% or much less than that?
A steel blade placed gently on the surface of water floats on it. If the same blade is kept well inside the water, it sinks. Explain.
Answer in one sentence.
Define strain.
A spiral spring is stretched by a weight. The strain will be:
A spring is stretched by applying a load to its free end. The strain produced in the spring is ______.
A mild steel wire of length 2L and cross-sectional area A is stretched, well within elastic limit, horizontally between two pillars (Figure). A mass m is suspended from the mid point of the wire. Strain in the wire is ______.
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;
| (a) |  |
| (b) |  |
| (c) |  |
The tension in the strings will be ______.
Consider two cylindrical rods of identical dimensions, one of rubber and the other of steel. Both the rods are fixed rigidly at one end to the roof. A mass M is attached to each of the free ends at the centre of the rods.
Consider a long steel bar under a tensile stress due to forces F acting at the edges along the length of the bar (Figure). Consider a plane making an angle θ with the length. What are the tensile and shearing stresses on this plane
- For what angle is the tensile stress a maximum?
- For what angle is the shearing stress a maximum?
A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that g = 3.1πms-2, what will be the tensile stress that would be developed in the wire?
The area of the cross-section of the rope used to lift a load by a crane is 2.5 × 10-4m2. The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross-section of the rope should be ______.
(take g = 10 ms-2)
The stress-strain graph of a material is shown in the figure. The region in which the material is elastic is ______.
What is the physical quantity defined as the internal restoring force per unit area of a body?
Strain is defined as the ratio of:
When an elastic body is in equilibrium in its altered shape, the magnitude of the external deforming force is:
