Question

A stone of mass 0.60kg is attached to one end of an aluminum wire of length 0.9m and 0.6mm diameter suspended vertically. If the stone is rotated in a horizontal plane in such a way that it makes angle 85° with the vertical what is the increase in length of the wire? (Young's modulus of aluminum=7×10^10Nm,take g=9.8ms, sin85°=0.9962 and cos85°=0.0872

Answer 1

$\frac{F}{A}=\frac{E\cdot\Delta l}{l}\to \Delta l=\frac{F\cdot l}{A\cdot E}$

$F\cos85^\circ=mg\to F=mg/\cos85^\circ=0.6\cdot9.8/\cos85^\circ=67.5\ (N)$

$\Delta l=\frac{F\cdot l}{A\cdot E}=\frac{67.5\cdot0.9}{(3.14\cdot0.0006^2/4)\cdot7\cdot10^{10}}=0.0031\ (m)=3.1\ (mm)$