Speed of Particle in Horizontal Circular Motion – Rankers Physics
Topic: Circular Motion
Subtopic: Dynamics of Circular Motion

Speed of Particle in Horizontal Circular Motion

A particle of mass \(m\) is tied to a string of length \(l\) and whirled into a horizontal plane. If tension in the string is \(T\) then the speed of the particle will be:

(1999)

\(\sqrt{\frac{Tl}{m}}\)
\(\sqrt{\frac{2Tl}{m}}\)
\(\sqrt{\frac{3Tl}{m}}\)
\(\sqrt{\frac{Tl}{2m}}\)

Solution:

Concept: Centripetal force is provided by the tension in the string.
Formula: Centripetal force \(F_c = \frac{mv^2}{l}\). Here, \(F_c = T\).
Solution: \(T = \frac{mv^2}{l}\). Rearranging for \(v\), we get \(v^2 = \frac{Tl}{m}\), so \(v = \sqrt{\frac{Tl}{m}}\).

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