Question

A particle is moving in a circular path of radius $r$ with an angular speed ${}^{\prime }{\omega }^{\prime }$. Suddenly, the radius is quadrupled and angular speed is halved. Then which of the following statements is correct?

• A. Centripetal force is doubled
• B. Centripetal force is halved
• C. Centripetal force remains same
• D. None of the above

Answer 1

The correct option is C Centripetal force remains same

For a particle moving in a circular path of radius '$r$' with an angular speed ${}^{\prime }{\omega }^{\prime }$, centripetal force is given by
$F=mr{\omega }^2$
Initially, $r_1=r,{\omega }_1=\omega$
$\Rightarrow F_1=m{r}_1{\omega }_1^2=mr{\omega }^2$
Finally, $r_2=4r,{\omega }_2=\frac{\omega }{2}$
$\Rightarrow F_2=m{r}_2{\omega }_2^2=m\left(4r\right){\left(\frac{\omega }{2}\right)}^2=mr{\omega }^2=F_1$
$\therefore$ centripetal force remains the same.