A mass m is revolving in a vertical circle at the end of a string of length 20 cm. By how much does the tension of the string at the lowest point exceed the tension at the top most point?

The tension T₁ at the topmost point is given by

${\mathrm{T}}_1=\frac{{{\mathrm{mv}}_1}^2}{20}-\mathrm{mg}$

Centrifugal force acting outward while weight acting downward.

The tension T₂ at the lowest point

${\mathrm{T}}_2=\frac{{{\mathrm{mv}}_2}^2}{20}+\mathrm{mg}$

centrifugal force and weight (both) acting downward

$\begin{array}{l}{\mathrm{T}}_2-{\mathrm{T}}_1=\frac{{\mathrm{mv}}_2^2-{\mathrm{mv}}_1^2}{20}+2\mathrm{mg}\\ {\mathrm{v}}_1^2={\mathrm{v}}_2^2-2\mathrm{gh}\\ \text{ or }{\mathrm{v}}_2^2-{\mathrm{v}}_1^2=2\mathrm{g}\left(40\right)=80\mathrm{g}\\ \therefore {\mathrm{T}}_2-{\mathrm{T}}_1=\frac{80\mathrm{mg}}{20}+2\mathrm{mg}=6\mathrm{mg}\end{array}$