A bob of mass m is suspended by a light string of length L.It is imparted a horizontal velocity v_{0}at the lowest point A such that it completes a semi- circular trajectory in the vertical plane with the string becoming slack only on reaching the topmost point,C.Obtain an expression for

i) v_{0}

ii)the speeds at point B and C

Hi,

Here is the answer to your query.

Given:

Mass of the bob=

*m*,Length of the string=

*L*,*v*

_{0}The tension force will not work on the bob as the displacement will always be perpendicular to the string.

At point A:

Total mechanical energy,

(As the potential energy is zero) …..1

The centripetal force for the circular motion will be,

At the highest point C, as the string slackens the tension becomes zero. Then,

The total energy,

So at A,

(Using 1)

Now, at B,

Hope, you got the answer.

Best wishes!!

**
**