Kinematics Question 545

Question: A weightless thread can bear tension upto 3.7 kg wt. A stone of mass 500 gms it’s tied to it and revolved in a circular path of radius 4 m in a vertical plane. If $ g=10m{{s}^{-2}} $ , then the maximum angular velocity of the stone will be[MP PMT/PET 1998]

Options:

A) 4 radians/sec

B)16 radians/sec

C) $ \sqrt{21} $ radians/sec

D) 2 radians/sec

Show Answer

Answer:

Correct Answer: A

Solution:

Max. tension that string can bear = 3.7 kgwt = 37N

Tension at lowest point of vertical

$ \text{loop}=mg+m{{\omega }^{2}}r $ = $ 0.5\times 10+0.5\times {{\omega }^{2}}\times 4=5+2{{\omega }^{2}} $ \ 37 = 5 + 2w2 therefore w = 4 rad/s.



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