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Consider two wires X and Y. The radius o...

Consider two wires X and Y. The radius of wire X is 3 times the radius of Y. If they are stretched by the same load then the stress on Y is

A

equal to that on X

B

thrice that on X

C

nine times that on X

D

Half that on X

Text Solution

Verified by Experts

The correct Answer is:
C
Stress = `F/A`
Stress on `X = (F_x)/(A) = (F_x)/(pir_x^2), "Stress on" Y = (F_y)/A = (F_y)/(pi r_y^2)`
If `F_x = F_y`, so, `r_x = 3r_y`
`(("Stress")_x)/("Stress")_(y) = (pi r_y^2)/(pi r_x^2) = (r_y^2)/(9 r_y^2)`
`("Stress")_(y) = 9 ("Stress")_(x)`
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