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 of its value, the corresponding minimum speed will be:

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

Answer 1

Answer: (B)

$\frac{v}{2}$

Velocity at lowest point is $\sqrt{5g\ell }$
$v\propto \sqrt{\ell }$
$\frac{v_1}{v_2}=\sqrt{\frac{{\ell }_1}{{\ell }_2}}=\sqrt{\frac{R}{R/4}}=\sqrt{4}$
$\Rightarrow v_2=\frac{v}{2}$