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A conical pendulum consists of a bob of mass m in motion in a circular path in a horizontal plane as shown in figure. During the motion, the supporting wire of length l, maintains a constant angle θ with the vertical. The magnitude of the angular mornentum of the bob about the vertical dashed line is

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a

(m2gl3cos4θsin θ)12

b

(m2gl3sin4θcos θ)12

c

(m2gl3sin3θcos θ)12

d

(m2gl3cos3θsin θ)12

answer is B.

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Detailed Solution

We start with the particle under a net force model in the x and y directions:∑ Fx = max :T sin θ = mv2r∑ Fy = may : T cos θ = mgSo sin θcos θ = v2rg and v = rgsin θcos θthen L = rmv sin 900 = rmrgsin θcos θ = m2gr3sin θcos θand since r = l sin θ,L = m2gl3sin4θcos θ

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A conical pendulum consists of a bob of mass m in motion in a circular path in a horizontal plane as shown in figure. During the motion, the supporting wire of length l, maintains a constant angle θ with the vertical. The magnitude of the angular mornentum of the bob about the vertical dashed line is