Question

A block of mass $m$ at the end of a string is whirled round in a vertical circle of radius $r$. The critical speed of the block at the top of its swing below which the string would slacken before block reaches the top is

• A. $\sqrt{2rg}$
• B. $\sqrt{3rg}$
• C. $\sqrt{rg}$
• D. $\sqrt{5rg}$

Answer 1

The correct option is C $\sqrt{rg}$

the string will not slack if the centrifugal force on the particle is greater then or equal to the weight of mass i.e.
$\frac{m{v}^2}{r}\ge mg\Rightarrow v\ge \sqrt{rg}\Rightarrow v_c=\sqrt{rg}$