In a conical pendulum the bob of mass ' m ' moves in a horizontal circle of radius ' r ' with uniform speed ' V '. The string of length ' L ' describes a cone o

Question

In a conical pendulum the bob of mass ' m ' moves in a horizontal circle of radius ' r ' with uniform speed ' V '. The string of length ' L ' describes a cone of semi vertical angle ' θ '. The centripetal force acting on the bob is ( g = acceleration due to gravity)

TestHub · Accepted Answer

​ T cos θ = mg sin θ = L r ​ cos θ = L L 2 − r 2 ​ ​ ​ ∴ T mr ω 2 L T × r ​ ω 2 ​ = cos θ mg ​ = L 2 − r 2 ​ mgL ​ = T sin θ = m 2 ... ( sin θ = L r ​ ) = L 2 − r 2 ​ g ​ ​ ∴ The centripetal force is F = L 2 − r 2 ​ mgr ​

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