Question

A stone of $0.5kg$ mass is attached to one end of a $0.8m$ long aluminium wire of $0.7mm$ diameter and suspended vertically. The stone is now rotated in a horizontal plane at a rate such that wire makes an angle of 85${}^o$ with the vertical. If Y $=$ 7x10${}^{10}$ Nm${}^{-2}$ , sin 85${}^o=$ 0.9962 and cos85${}^o=$ 0.0872 , the increase in length of wire is

• A. 1.67x10${}^{-3}$m
• B. 6.17x10${}^{-3}$m
• C. 1.76x10${}^{-3}$m
• D. 7.16x10${}^{-3}$m

Answer 1

The correct option is A 1.67x10${}^{-3}$m

By equating force in vertical direction

$Tcos{85}^{\circ }=mg$

$T=\frac{mg}{Cos{85}^{\circ }}$

$y=\frac{F/A}{△l/l}$

$△l=\frac{Fl}{△Y}$

$=\frac{mgl}{AYCos{85}^{\circ }}$

$=1.7\times {10}^{-3}m$

$\simeq 1.67\times {10}^{-3}m$