Question

Two spheres of equal masses are attached to a string of length 2 m as shown in figure. The string and the spheres are then whirled in a horizontal circle about O at a constant rate. What is the ratio of tension in the string between P and Q to tension in the string between P and O)?

• A. $\frac{1}{2}$
• B. $\frac{2}{3}$
• C. $\frac{3}{2}$
• D. $2$

Answer 1

The correct option is B $\frac{2}{3}$

$\begin{array}{c}mg\cos \theta -N=\frac{m{v}^2}{R}\\ whenthebodywilllosscontact,\\ N=0\\ So,\\ mg\cos \theta =m\frac{v^2}{R}\\ or{v}^2=gR\cos \theta \\ fromthefigure,\\ \cos \theta =\frac{h}{R}\\ or,h=R\cos \theta \\ Thus,v^2=gh\\ Accordingtolowofconservationofenergy,\\ TotalenergyatA=totalenergyatB\\ mgR=\frac{1}{2}m{v}^2+mgh\\ orR=h\left(1+\frac{1}{2}\right)=\frac{3}{2}h\\ so,H=\frac{2}{3}R\\ Hence,\\ optionBiscorrectanswer.\end{array}$