Q 11-08-089JEE MainJEE Main 2020 (9 Jan, Shift 1)Easy
A body of mass $m = 10$ kg is attached to one end of a wire of length $0.3$ m. What is the maximum angular speed (in rad s$^{-1}$) with which it can be rotated about its other end in a space station without breaking the wire? [Breaking stress of wire $(\sigma) = 4.8\times10^7$ N m$^{-2}$ and area of cross-section of the wire $= 10^{-2}$ cm$^2$]
Numerical value type. Enter your answer.
Answer: 4
Maximum tension $= \sigma A = 4.8\times10^7\times10^{-6} = 48$ N.
In a space station there is no weight, so the tension alone provides the centripetal force:
$$m\omega^2 L = 48 \Rightarrow \omega^2 = \frac{48}{10\times0.3} = 16 \Rightarrow \omega = 4\ \text{rad s}^{-1}$$
Solution by Sreeraj P, M.Sc Physics