Question

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

• A. 2 mg
• B. 4 mg
• C. 6 mg
• D. 8 mg

Answer 1

Answer: (C)

The tension $T_1$ at the topmost point is given by
$T_1=\frac{m{v}_1^2}{20}-mg$
Centrifugal force acting outward while weight acting downward.
The tension $T_2$ at the lowest point
$T_2=\frac{m{v}_2^2}{20}+mg$
Centrifugal force and weight (both) acting downward
$T_2-T_1=\frac{m{v}_2^2-m{v}_1^2}{20}+2mg$
$v_1^2=v_2^2-2gh$
or $v_2^2-v_1^2=2g(40)=80g$
$\therefore T_2-T_1=\frac{80mg}{20}+2mg=6mg$