Question

The breaking tension of a string is 10 N. A particle of mass 0.1 kg tied to it is rotated along a horizontal circle of radius 0.5 metre. The maximum speed with which the particle can be rotated without breaking the string is-

• A. $\sqrt{5}m/sec$
• B. $\sqrt{\left(50\right)}m/sec$
• C. $\sqrt{\left(500\right)}m/sec$
• D. $\sqrt{\left(1000\right)}m/sec$

Answer 1

The correct option is B $\sqrt{\left(50\right)}m/sec$

$\begin{array}{c}\text{Given,}m=0.1kg\text{and}l=0.5m\\ \text{Also, breaking tension of string is}10N\text{.}\\ \text{for maximum speed, string must be at its breaking}\\ \text{tension.}\end{array}$

$\text{Thus,}\begin{array}{cc}{\text{T}}_{breaking}& =\frac{m{V}_{max}^2}{l^{}}\\ \Rightarrow 10& =\frac{0.1\times V_{max}^2}{0.5}\\ & \therefore V_{max}=\sqrt{50}m/s\end{array}$