Question

A ball of mass m is attached with a light string of length $\ell$ and released from position 1. String becomes taut at position 2 and reaches the lowest position 3, then find the velocity of the ball after the strings become taut.

Answer 1

The mass $=m$

Length$=l$

The acceleration of the string is $\frac{v^2}{r}$ and the force due to tension $T$ is $T\frac{dl}{r}$ where $dl$ is the length of an element of string. Both directed towards the centre of curvature

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

(m being mass/unit length)

then there is no need for the tube.

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