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Question
In a conical pendulum, a string of length 120 cm is fixed at rigid support and carries a mass
of 150 g at its free end. If the mass is revolved in a horizontal circle of radius 0.2 m around a
vertical axis, calculate tension in the string (g = 9.8 m/s2)
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Solution
l = 120 cm = 1.2 m,
r = 0.2 m,
m = 150 g = 150 × 10−3 kg = 0.15 kg
Tension in the supporting thread (T)
By Pythagoras theorem,
l2 = r2 + h2
h2 = l2 − r2
h2 = 1.44 − 0.04 = 1.4
∴ h = 1.1 83 m
The weight of bob is balanced by vertical component of tension T
∴ T cos θ = mg
cos θ = `h/l = 1.183/1.2` =0.9858
∴ T = 1.491 N
The tension in the string is 1.491 N.
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