Question

A ball of mass $1\text{kg}$ is tied to one end of a string of length $1\text{m}$, pivoting the other end of string, ball is rotated at an angular speed of $2\text{rev/min}$. The tension in the string is

• A. $0.4\text{N}$
• B. $0.04\text{N}$
• C. $40\text{N}$
• D. $4\text{N}$

Answer 1

The correct option is B $0.04\text{N}$

Given, mass of a ball $\left(m\right)=1\text{kg}$
Length of string $\left(l\right)=1\text{m}$
Angular speed $\left(\omega \right)=2\text{rev/min}=2\times \frac{2\pi }{60}=\frac{\pi }{15}\text{rad/sec}$

Since, tension provides necessary centripetal force

Tension in the string $\left(T\right)=ml{\omega }^2$
$T=1\times 1\times {\left(\frac{\pi }{15}\right)}^2=0.04\text{N}$ $(\because l=1\text{m})$

Hence option B is the correct answer