Question

A particle of mass $7 \,kg$ is executing circular motion with time period of $11\, sec$. Find out centripetal force if radius of circle is $10\, m$.

• A. $\frac{30}{7} N$
• B. $\frac{40}{7} N$
• C. $30\, N$
• D. $\frac{160}{7}\, N$

Answer 1

Answer: (D)

As we know, $\omega 2\pi f$
$\omega=\frac{2\pi}{T}\quad\quad\quad\quad\quad\left[\because \,f=\frac{1}{T}\right]$
And, $v = r\omega$
Then, $v = \frac{2\pi r}{T}$
$v = \frac{2\pi\left(10\right)}{11}=\frac{2\times22\times10}{7\times11}=\frac{40}{7}$
Centripetal force,
$F_{c}=\frac{mv^{2}}{r}=\frac{7}{10}\times\frac{40}{7}\times\frac{40}{7}=\frac{160}{7}N$