A block of weight 10 N is fastened to one end of a wire of cross sectional area `3 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 `2ms^-1`. Find the elongation of the wire when the block is at the bottom of the circle. Young modulus of the material of the wire `=2xx10^11Nm^-2`.

Explanation

Forces acting on the block are a the tension T and b. the weight W. At the lowest point, the resultant force is T-W towards the centre. As the block is goigin a circle, the net force towards the centre should be `mv^2/r` with usual symbols. Thus,
`TW=mv^2/r`
`T=W+mv^2/r`
`=10n=((1kg)(2ms^-1)^2)/(0.2m)=30N`
`We have Y=(T/A)/(l/L)`
`or l=(TL)/(AY)`
`=(30Nxx(20cm))/((3xx10^-6m^2)x(2xx10^11Nm^-2))`
`=5xx10^-5xx20cm=10^-3cm.