A ball is revolving in a horizontal circle by attaching it to a string. the velocity of a ball changes continuously. it means acceleration exist. can we say the tension force in string does not work on ball because acceleration exist? Explain. 

Dear Student,

Suppose an object of mass 'm' is tied to the end of an inextensible string and whirled in a vertical circle of radius 'r'.
There is tension in the string.We consider tension at the highest point A and lowest point B.

Highest point A:
Forces acting on the object at A:
Tension T1 acting in downward direction.
Weight mg acting in downward direction
Here the centripetal force is provided partly by weight and partly by tension in the string.
$$\begin{gathered} {\mathrm{T}}_1+\mathrm{mg}=\frac{{{\mathrm{mv}}_1}^2}{\mathrm{r}} \\ \mathrm{or}\mathbf{ }{\mathbf{T}}_{\mathbf{1}}\mathbf{=}\frac{{{\mathbf{mv}}_{\mathbf{1}}}^{\mathbf{2}}}{\mathbf{r}}\mathbf{-}\mathbf{mg} \end{gathered}$$

Lowest point B,
Forces acting are:
1-Tension T2 acting in upward direction
2-Weight mg acting in downward direction
At this point,
$$\begin{gathered} {\mathrm{T}}_2-\mathrm{mg}=\frac{{{\mathrm{mv}}_2}^2}{\mathrm{r}} \\ \mathrm{or} {\mathbf{T}}_{\mathbf{2}}\mathbf{=}\frac{{{\mathbf{mv}}_{\mathbf{2}}}^{\mathbf{2}}}{\mathbf{r}}\mathbf{+}\mathbf{mg} \end{gathered}$$

Regards.