Question

The upper end of a wire $1m$ long and $2mm$ radius is clamped. The lower end is twisted through angle ${45}^o$. What is the angle of twist?

• A. ${0.009}^o$
• B. ${0.09}^o$
• C. ${0.9}^o$
• D. $9^o$

Answer 1

The correct option is C ${0.9}^o$

$\begin{array}{c}\text{Given, wire of length}=1m\\ \text{radius}=2\times {10}^{-3}m\end{array}$

$\begin{array}{c}\text{Since, the radius is very}\\ \text{small. So, in this case}\\ \tan \varphi \simeq \varphi \\ \text{Also,}AB=r\theta \text{( radius is}\\ \text{very small)}\end{array}$

$\begin{array}{cc}\tan \varphi & =\frac{r\theta }{1}\\ \varphi & =\frac{2\times {10}^{-3}\times 45}{1}={0.9}^{\circ }\end{array}$