Question

What happens to centripital force of a revolving body if you double the orbital speed v and halve the angular velocity $\omega$ :-

• A. Centripetal force remains uncharged
• B. Centripetal force is halved
• C. Centripetal force is doubled
• D. centripetal force is quadrupled

Answer 1

The correct option is A Centripetal force remains uncharged

Here Initial centripetal acceleration, $a_1=\frac{v^2}{r}$

$v_2=2v{\omega }_2=\frac{\omega }{2}$

but r = $\frac{v}{\omega }$

$r_2=\frac{v_2}{{\omega }_2}=\frac{2v}{\left(\omega /2\right)}=\frac{4v}{\omega }=4r$

$a_2=\frac{(2v{)}^2}{r_2}$

$a_2=\frac{4v^2}{4r}=\frac{v^2}{r}=a_1$

So, Centripetal acceleration is unchanged

Hence Centripetal force remains unchanged