Question

A string can bear a maximum tension of $3.16kg-wt$. What maximum number of revolutions per second can be made by a stone of mass $49g$ tied to one end of a $1m$ long piece of this string so that the string may not break? ($\pi =22/7$)

Answer 1

length of string,$r=1m$

the maximum tension in the string $T=3.16kg-wt$

$=3.16\times 10$

$T=31.6N$

mass of stone $m=49g=0.049kg$

the maximum tension in the string,$T=\frac{m{v}^2}{r}+mg$

$\begin{array}{c}\Rightarrow 31.6=\frac{0.049\times v^2}{12}+0.049\times 10\\ \Rightarrow 31.6=0.049v^2+0.49\\ \Rightarrow v^2=\frac{31.6-0.49}{0.049}\\ \Rightarrow v^2=\frac{31.11}{0.049}\\ \Rightarrow v=\sqrt{634.89}\\ \Rightarrow v=25.19m/s\end{array}$

$\begin{array}{c}v=rw\\ w=\frac{v}{r}=\frac{25.19}{1}=25.19\\ w=2\pi n\\ n=\frac{w}{2\pi }=\frac{25.19}{2\times 3.14}=\frac{25.19}{6.25}=4.01\\ n=4.01\end{array}$