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Question

In the figure shown below, a string of length l is connected to a bob of mass m and is moving around a vertical axis through a fixed point. Then which of the following statements is (are) correct?


A
Angle of inclination of the string is equal to cos1(glω2)
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B
Angle of inclination of the string is equal to sin1(glω2)
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C
Tension in the string is equal to T=mlω2
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D
Tension in the string is equal to T=m(ltanθ)ω2
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Solution

The correct option is C Tension in the string is equal to T=mlω2
From FBD of the bob:

Tsinθ balances the weight of the bob and Tcosθ provides necessary centripetal force.
Tsinθ=mg ... (1)
Tcosθ=mRω2... (2)
Here, R=lcosθT=mlω2 ... (3)
From (1) & (3)
sinθ=mgT=mgmlω2
θ=sin1(glω2)

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