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Question

A small sphere of mass 200 gm is attached to an inextensible string of length 130 cm whose upper end is fixed to the ceiling. The sphere is made to describe a horizontal circle of radius 50 cm. Calculate the time period of this conical pendulum and the tension in the string. (π2=10)

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Solution

m=200g

l=130cm=1.3m

So the time period of a pendulum doesn't depend on the mass of the Bob. It is equal to :

2πlg

where l is length and g is gravity. Which gives us:

2t=(4π2)×1.39.8 (squaring both sides)

π2and 9.8 are approx the same so we can cut it out, giving us:

(4)×(1.3)=520s

Therefore 2t=5.2s

t=2.29s

the force on the string is simple mg=(200)×(10)=2000 gm/s

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