Question

A string of length $1\text{m}$ is fixed at one end and carries a mass of $100\text{g}$ at the other end. The string makes $\left(2/\pi \right)$ revolutions per second around vertical axis through the fixed end. What is the tension in the string :-

• A. $1.6\text{N}$
• B. $0.8\text{N}$
• C. $3.2\text{N}$
• D. $2.4\text{N}$

Answer 1

The correct option is A $1.6\text{N}$

Equating forces
$T\sin \theta =m\times v\times v/r...\left(1\right)$
$T\cos \theta =m\times g...\left(2\right)$
$\omega =2/\pi \times 2\pi =4\text{rad}$
From 1 and 2
$\tan \theta =v^2/rg={\omega }^{2}r/g$
$\sin \theta =r$
$\tan \theta =4^2\times \left(\sin \theta \right)/g$
$\sin \theta /\cos \theta =16\times \sin \theta /10$
$1/\cos \theta =1/1.6=0.625...\left(3\right)$

From (3)
$T=mg/\cos \theta =(0.1\times 10)/\left(1/1.6\right)$
$T=1.6\text{N}$