A block of weight 10 N is fastened to one end of wire of cross-sectional area `4 mm^(2)` and is rotated ina vertical circle of radius 30 cm. The speed of the block at the bottom of the circle is `3 ms^(-1)`. Find the elongation of the wire when the block is at the bottom of the circle . Young's modulus of the material of the wire `=2xx10^(11)Nm^(-2).(g=10ms^(-2))`

Explanation

Given, mass m =100 N
Area `A=4 mm^(2)`
Radius R=30 cm
Speed of block `v=3 ms^(-1)`

Tension of the wire
`T-mg=(mv^(2))/(R)` or `T=mg+(mv^(2))/(R)=100+(10xx3^(2))/(0.3)=400N`
The elongation of the wire when the block is at the bottom of the circle
`Y=(FR)/(ADeltaL)`
Here force (F) is equal ot the tension in the wire
So, `Y=(TR)/(ADeltaL)`
`DeltaL=(TR)/(AY)=(400xx0.3)/(4xx10^(-6)xx2xx10^(11))=1.5xx10^(-4)m`