Question

A body of mass $500\text{g}$ is moving in a circular path of radius $\frac{10}{{\pi }^2}\text{cm}$ with an angular speed of $2\pi \text{rad/s}$. The centripetal force is

• A. $0.1\text{N}$
• B. $0.2\text{N}$
• C. $0.3\text{N}$
• D. $40\text{N}$

Answer 1

The correct option is B $0.2\text{N}$

Given, mass of a body $\left(m\right)=500\text{g}=0.5\text{kg}$
Radius of circular path $\left(r\right)=\frac{10}{{\pi }^2}\text{cm}=\frac{10}{{\pi }^2}\times {10}^{-2}\text{m}$
Angular speed $=2\pi \text{rad/s}$

To find centripetal force:
$F_c=mr{\omega }^2$
$F_c=0.5\times \frac{10}{{\pi }^2}\times (2\pi {)}^2\times {10}^{-2}$
$F_c=\frac{10}{2{\pi }^2}\times 4{\pi }^2\times {10}^{-2}$
$F_c=20\times {10}^{-2}\text{N}$
$F_c=0.2\text{N}$

Hence option B is the correct answer.