Question

A particle is projected so as to just move along a vertical circle of radius $r$ with the help of the massless string. The ratio of the tension in the string when the particle is at the lowest and highest point on the circle is?

• A. $1$
• B. Finite but large
• C. Zero
• D. Infinite

Answer 1

The correct option is D Infinite

$T-mg\cos \theta =\frac{m{V}^2}{r}$

At lowest point $A$:

$T_A=\frac{m{V}_A^2}{r}+mg\cos \left(0^o\right)$

$⟹T_A=\frac{m{V}_A^2}{r}+mg$

At highest point $B$:

$T_B=0$

$\therefore \frac{T_A}{T_B}=\frac{\left(m{V}_A^2/r\right)+mg}{0}$

$⟹\frac{T_A}{T_B}=\infty$