Question

A mass is attached to the end of a string of which is tied to a fixed point O. The mass is released from the initial horizontal position of the string. Below the point O at what minimum distance a peg P be should fixed so that the mass tums about P and can describe a complete circle in the vertical plane?

• A. $\left(\frac{3}{5}\right)l$
• B. $\left(\frac{2}{5}\right)l$
• C. $\frac{l}{3}$
• D. $\frac{2l}{3}$

Answer 1

The correct option is A $\left(\frac{3}{5}\right)l$

$\begin{array}{c}v=\sqrt{2gl}...........\left(1\right)\\ forcompletingthecirculargroundP\\ v=\sqrt{5g\left(l-d\right)}=\sqrt{2gl}\\ \Rightarrow 5g\left(l-d\right)=2gl\\ \Rightarrow 5l-5d=2l\\ \Rightarrow 3l=5d\\ \Rightarrow d=\frac{3l}{5}\\ \therefore optionAiscorrectanswer.\end{array}$