A mass m is revolving in a vertical circle

Asked by admin @ 23/08/2021 in Physics viewed by 368 People

a mass M is revolving in a vertical circle at the end of a string of length 20 CM by how much year does the tension of the string at the lowest point exceed the tension at the top most point.

Answered by admin @ 23/08/2021

Let tension $T_1$ at the topmost point is given by,
$T_1+mg=\frac{mv_1^2}{l}$ .....(1)
here tension and weight of body acting towards centre of circle and balancing centrifugal force acting outward. here l is length of string.

similarly, The tension $T_2$ at the lowest point is given by,
$T_2-mg=\frac{mv_2^2}{l}$ .....(2)
here, tension acting inward while balancing centrifugal force and weight of body acting outward.

$T_2-T_2=\frac{mv_2^2}{l}+mg-\frac{mv_1^2}{l}+mg\\\\=\frac{m}{l}(v_2^2-v_1^2)+2mg$

we know,from law of kinematics equation,
$v_1^2=v_2^2-2g(2l)$

$T_2-T_1=\frac{m}{l}\{2g(2l)\}+2mg\\\\=6mg$

hence, answer is 6mg

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