Question

A particle is moving in a vertical circle. The tensions in the string when passing through two positions at angle $30^{\circ}$ and $60^{\circ}$ from vertical (lowest position) are $T_{1}$ and $T_{2}$ respectively, then

• A. $T_{1}=T_{2}$
• B. $T_{1} >\,T_{2}$
• C. $T_{1} <\,T_{2}$
• D. Tension in the string always remains the same

Answer 1

Answer: (B)

$T =\frac{ mv ^{2}}{ r }+ mg \cos \theta$
For $\theta=30^{\circ}$,
$T _{1}=\frac{ mv ^{2}}{ r }+ mg \cos 30^{\circ}=\frac{ mv ^{2}}{ r }+\frac{\sqrt{3} mg }{2}\, \dots(i)$
For $\theta=60^{\circ}$
$T _{2}=\frac{ mv ^{2}}{ r }+ mg \,\cos 60^{\circ}=\frac{ mv ^{2}}{ r }+\frac{ mg }{2}\, \dots(ii)$
From equation (i) and (ii), we can say
$\therefore T _{1} >\, T _{2}$