Question

A body attached to a string of length describes a vertical circle such that it is just able to cross the highest point. Find the minimum velocity at the bottom of the circle.

• A. $\sqrt{2gL}$
• B. $\sqrt{gL}$
• C. $\sqrt{3gL}$
• D. $\sqrt{5gL}$

Answer 1

The correct option is B $\sqrt{gL}$

Radius of the circle traced will be equal to the length of the string

In circular motion tension in the string is balanced by the centripetal force

hence we know that,

$T=\frac{m{v}^2}{r}$

$T=\frac{m{v}^2}{L}$

Velocity at any point,$V=\sqrt{\frac{TL}{m}}$

And at lowest point the tension is balanced by the weight of the block

∴∴ tension = weight = mg

$V=\sqrt{\frac{mgL}{m}}=\sqrt{gL}$