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JEE Main 2021 (25 Feb, Shift 1) · Vertical Circle: Speed & Tension

Vertical Circle: Speed & Tension question from JEE Main 2021 (25 Feb, Shift 1)

Q15JEE Main 2021 · 25 FEB · SHIFT 1Medium

Vertical Circle: Speed & Tension

A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio 5: 1. The velocity of the bob at the highest position is ________ m/s. (Take g = 10 m/s2)

Numerical answer type. Work it out, then open the answer.

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Answer: 5

For a vertical circle: $T_{max} - T_{min} = 6mg$
$T_{max} = 5T_{min} \Rightarrow 4T_{min} = 6mg \Rightarrow T_{min} = 1.5mg$
At the top: $T_{min} + mg = \frac{mv^2}{l} \Rightarrow v^2 = 2.5gl = 25$
$v = 5$ m/s

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