Question

A particle of mass m attached to the end of string of length l is released from the horizontal position. The particle rotates in a circle about O as shown. When it is vertically below O, the string makes contact with a nail N placed directly below O at a distance h and rotates around it. For he particle to swing completely around the nail in a circle.

• A. (a) $h<\frac{3}{5}l$
• B. (b) $h\ge \frac{3}{5}l$
• C. (c) $h<\frac{2}{5}l$
• D. (d) $h\ge \frac{2}{5}l$

Answer 1

Answer: (B)

(b) $h\ge \frac{3}{5}l$

Speed required for complete circle

[B] $V\ge \sqrt{5\times g\times \left(l-h\right)}$

and velocity of particle at bottom

$\begin{array}{c}V=\sqrt{2gl}\\ So,2gl\ge 5g\left(l-h\right)\\ h\ge \frac{3}{5}l\end{array}$