Question

The minimum speed for a particle at the lowest point of a verticle circle of radius $R$ to describe 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)

$\frac{V}{2}$

Minimum speed for a particle at the lowest point of a vertical circle is given by
$V=\sqrt{5gr}$
where, g is the acceleration due to gravity & r is the radius of the circle.
Thus, $V\propto \sqrt{r}$
Hence when radius is reduced to one-fourth V will reduce by half.