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A block of mass 1 kg is fastended to one...

A block of mass 1 kg is fastended to one end of a wire of cross-sectional area 2 `mm^(2)` and is rotated in a vertical circle of radius 20 cm. The speed of the block at the bottom of the circle is 3.5 `ms^(-1)`. Find the elongation of the wire when the block is at the top of the circle.

Text Solution

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(i) Tension at the bottom of the circle,
`T=(mv^(2))/(r )+mg=(1xx(3.5)^(2))/(0.2) +1xx9.8`
`=61.25+9.8=71.05N`
This tension in the string is equal to the force, F i.e. F = 71.05N, L = r = 0.2m.
The increase in length,
`e=(FL)/(AY)=(71.05xx0.2)/(2xx10^(-6)xx2xx10^(11))=3.553xx10^(-5)m`
(ii) Tension at the top of the circle,
T = Tension at the bottom - 6 mg
`=71.05-6xx1xx9.8`
`=71.05-58.8=12.25N`.
`F=12.25N, L=0.2m`.
The increase in length
`e=(FL)/(AY)=(12.25xx0.2)/(2xx10^(-6) xx 2xx10^(11))=0.6125xx10^(-5)m`
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