Question

The minimum speed for a particle at the lowest point of a vertical circle of radius R, to describe the circle is ‘v’. If the radius of the circle is reduced to one-fourth its value, the corresponding minimum speed will be

• A. $\frac{v}{4}$
• B. $\frac{v}{2}$
• C. 2v
• D. 4v

Answer 1

Answer: (B)

$\frac{v}{2}$

Answer 2

$v = \sqrt{5gr}$ $\therefore v \propto \sqrt{r}$ So $\frac{v_{2}}{v_{1}} = \sqrt{\frac{r_{2}}{r_{1}}} = \sqrt{\frac{r/4}{r}} = \frac{1}{2}$

⇒ $v_{2} = v/2$