Question

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

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

Answer 1

Answer: (C)

$6mg$

Let tension $T_1$ at top most point is given by

$T_1+mg=\frac{m{V}_1^2}{l}$ ...(1)

similarly, the tension $T_2$ at the lowest point is given by

$T_2-mg=\frac{m{V}_2^2}{l}$ ...(1)

here, tension acting in words while balancing centrifugal force and weight of the body acting outwards

$T_2-T_1=\frac{m{v}_2^2}{l}+mg-\frac{m{v}_1^2}{l}+mg$

$\frac{m}{l}(v_2^2-V_1^2)+2mg$

we know from kilometres

$v_1^2=v_2^2-2g\left(2l\right)$

$T_2{T}_1=\frac{m}{l}\left[2g\right(2l\left)\right]+2mg$

$=6mg$

Hence (C) is correct answer