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A mass of 2kg is suspended from a fixed ...

A mass of 2kg is suspended from a fixed point by a wire of length 3m and diameter 0.5 mm. Initially the wire is just unstretched, the mass resting on a fixed support. By how much must the temperature fall if the mass is to be entirely supported by the wire? Given that Y of the wire = 206 G Pa, `alpha=11xx10^(-6)//""^(@)C`.

Text Solution

Verified by Experts

When the temperature decreases the wire contracts in length and lifts the mass up. But the weight begins to produce a stress and counteracts the contraction produced. Hence the contraction due to cooling is equal to the stretching produced by the weight W.
`thereforeDeltaL=(WL)/(AY)=(2xx9.8xx3)/(pi(0.25)^(2)xx10^(-6)xx206xx10^(9))`
Now the contraction due to cooling
= `Lalphad theta=3xx11xx10^(-6)xxd theta`
Since the contraction due to cooling = extension produced by the weight. On solving `d theta=44^(@)C`
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