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Q.

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

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a

π5sec⁡

b

2π10sec⁡

c

2π5sec⁡

d

π10sec⁡

answer is B.

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Detailed Solution

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 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