Question

A wire of length $l=0.3m$ and area of cross-section ${10}^{-2}c{m}^2$ and breaking stress $4.8\times {10}^{7}N/m^2$is attached with a block of mass $10kg$. Find the maximum possible value of angular velocity with which block can be moved in a circle with a string fixed at one end.

Answer 1

Step 1. Given data

Length of wire $l=0.3m$

Area of cross-section $A={10}^{-2}c{m}^2={10}^{-6}{m}^2$

Stress $\sigma =4.8\times {10}^{7}N/m^2$

Mass of block $m=10kg$.

Step 2. Finding angular velocity $\omega$

Stress is given by $\sigma =\frac{F}{A}$

Force is

$$\begin{gathered} F=m{\omega }^{2}l \\ \Rightarrow \sigma =\frac{m{\omega }^{2}l}{A} \\ \Rightarrow 4.8\times {10}^7=\frac{10\times 0.3{\omega }^2}{{10}^{-6}} \\ \Rightarrow {\omega }^2=\frac{4.8\times 10}{3}=16 \\ \Rightarrow \omega =4rad/sec \end{gathered}$$

Hence answer is $\omega =4rad/sec$.