Advertisements
Advertisements
Question
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 ______.
Options
`x^2/(2L^2)`
`x/L`
`x^2/L`
`x^2/(2L)`
Solution
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 `underline(x^2/(2L^2))`.
Explanation:
Consider the diagram below
Hence, change in length
ΔL = BO + OC – (BD + DC)
= 2BO – 2BD .......(∵ BO = OC, BD = DC)
= 2(BO – BD)
= `2[(x^2 + L^2)^(1/2) - L]`
= `2L[(1 + x^2/L^2)^(1/2) - 1]`
= `2L[1 + 1/2 x^2/L^2 - 1]`
= `x^2/L` ........[∵ x << L]
Strain = `(ΔL)/(2L)`
= `(x^2/L)/(2L)`
= `x^2/(2L^2)`
APPEARS IN
RELATED QUESTIONS
A steel cable with a radius of 1.5 cm supports a chairlift at a ski area. If the maximum stress is not to exceed 108 N m–2, what is the maximum load the cable can support?
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.
Determine the volume contraction of a solid copper cube, 10 cm on an edge, when subjected to a hydraulic pressure of 7.0 ×106 Pa.
A mild steel wire of length 1.0 m and cross-sectional area 0.50 × 10–2 cm2 is stretched, well within its elastic limit, horizontally between two pillars. A mass of 100 g is suspended from the mid-point of the wire. Calculate the depression at the midpoint.
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.
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.
A heave uniform rod is hanging vertically form a fixed support. It is stretched by its won weight. The diameter of the rod is
The maximum load a wire can withstand without breaking, when its length is reduced to half of its original length, will ______.
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.
The value of tension in a long thin metal wire has been changed from T1 to T2. The lengths of the metal wire at two different values of tension T1 and T2 are l1 and l2 respectively. The actual length of the metal wire is ______.
