Two wires P and Q of same length and material but radii in the ratio 2:1 are suspended from a rigid support. Find the ratio of strain produced in the wires when: (i) both are under same stress (ii) both are loaded by same weight.

Solution

Given the radii of two wires is of the ratio 2:1.
Using the formula as per Hooke's law,

$Strain \propto Stress = \frac{Load}{Area} = \frac{F}{{πr}^{2}} a n d r_{P} : r_{Q} = 2 : 1$

i) When both the wires are under the same stress, strain produced will be the same.

ii) When both the wires are loaded by the same weight, then

$\frac{S t r a i n_{p}}{S t r a i n_{Q}} = \frac{(r_{Q})^{2}}{(r_{P})^{2}} = \frac{1}{4}$

Some More Questions From Mechanical Properties of Fluids Chapter

Name the property of material that opposes the deformation in it.

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Mechanical Properties Of Fluids

Two wires P and Q of same length and material but radii in the ratio 2:1 are suspended from a rigid support. Find the ratio of strain produced in the wires when: (i) both are under same stress (ii) both are loaded by same weight.

Some More Questions From Mechanical Properties of Fluids Chapter

Name the property of material that opposes the deformation in it.

Name the quantity which has neither unit nor dimensions.

Why strain is dimensionless?

What is stress?

Name the two types of stress.

What is tensile stress?

What is compression stress?

Define tangential stress.

What type of stress is set up in the body when the deforming force produces longitudinal strain or volumetric strain?

What type of stress is set up in the body when deforming force produces sheer strain?

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