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A copper wire of negligible mass, 1 m le...

A copper wire of negligible mass, `1 m` length and cross-sectional area `10^(-6) m^(2)` is kept on a smooth horizontal table with one end fixed. A ball of mass `1 kg` is attached to the other end. The wire and the ball are rotating with an angular velocity of `20 rad//s`. If the elongation in the wire is `10^(-3) m`.
a. Find the Young's modulus of the wire (in terms of `xx 10^(11) N//m^(2)`).
b. If for the same wire as stated above, the angular velocity is increased to `100 rad//s` and the wire breaks down, find the breaking stress (in terms of `xx 10^(10) N//m^(2)`).

A

`10^(9) N//m^(2)`

B

`10^(10) N//m^(2)`

C

`3 xx 10^(10) N//m^(2)`

D

`2 xx 10^(9) N//m^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Breaking Force F = Centrifugal Force `= m r omega^(2)`
`:.` Breaking Stress `= (F)/("Area") = (m r omega^(2))/("Area")`
`= (1 xx 1 xx 100 xx 100)/(10^(-6))`
Breaking Stress `= 10^(10) N//m^(2)` or Pa
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