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Questions  

A small sphere is suspended by a string of length 3m. If the sphere rotates in a horizontal circle of radius  2m with uniform speed, the time period of rotation of the sphere is 

a
π5sec⁡
b
2π10sec⁡
c
2π5sec⁡
d
π10sec⁡

detailed solution

Correct option is B

Tsin⁡θ=mω2r=mω2(lsin⁡θ)⇒T=mω2l.......(1)Also, Tcos⁡θ=mg.......(2)∴ ω2lcos⁡θ=g⇒ω=glcos⁡θ∴ Time period of rotation, T1=2π10=2π2×cos60o10sec=2π110sec

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A string of length l = 1 m is fixed at one end and carries a mass of 100 gm at other end. The string makes 5/π revolution per second about a vertical axis passing through its second end. What is the angle of inclination of the string with the vertical?


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