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A copper wire of negligible mass of leng...

A copper wire of negligible mass of length 1 m 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 revolving with an angular velocity of `20 rad.s^-1`. IF the elongation in the length of the wire is `10^-3m`, obtain the Young's modulus. IF on increasing the angular velocity to `100 rad .s^-1` the wire breaks down, obtain the breaking stress.

Text Solution

Verified by Experts

The stretching force developed in the wire due to the revolution of the ball is,
`F=(mv^2)/r=mromega^2=1times1times(20)^2=400N`
Stress in the wire `=F/A=400/10^-6=4times10^8N.m^-2`
Strain in the wire=`10^3/1=10^-3`
`therefore` Young.s modulus =`(stress)/(stra i n)=(4times10^8)/10^-3=4times10^11N.m^-2`
If the breaking angular velocity be `omega_0` then breaking stress
`=(mromega_0^2)/A=(1times1times(100)^2)/10^-6=1times10^10 N.m^-2`
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