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1)

A ball of mass (m)0.5 kg is attached to the end of a string having a length (L)0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in rad/s) is

28112021226_u2.PNG


A) 9

B) 18

C) 27

D) 36

Answer:

Option D

Explanation:

 

 29112021594_k1.PNG

 

T cosθ component will cancel mg

 Tsinθ  component will provide necessary centripetal force to the ball towards  centre C

    Tsinθ=mrω2=m(lsinθ)ω2

    ω=Tml

 or    ωmax=Tmaxml=3240.5×0.5

 =36 rad/s

    correct option is (d) 

 

Analysis of Question
(i) Question is simple

(ii) This is called the conical pendulum

(iii)The interesting fact in this problem is that ω or T is independent of  θ

 ωT

 If ω  is increased, T will also increase