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Asked by parikshitsingh854 | 27 Jul, 2019, 11:36: AM
answered-by-expert Expert Answer
Figure shows the various force acting the block of mass m.
T is centripetal force acting along rod due to circular motion.
f is friction force that prevents the slipping of mass on the plate.
Right side of figure shows the free body diagram
 
we have, normal reaction force,  N = mg + T sinθ  ...................(1)
 
Using eqn.(1) for normal reaction force, we have, for no slipping,  T cosθ = μ ( mg + T sinθ ) ..................(2)
 
Hence , centripetal force T is obtained from eqn.(2) as,  T = μ m g / ( cosθ - μ sinθ ) ................(3)
 
By substituting Centripetal force  T = m ω2 l   in eqn.(3),  
 
we get maximum angular velocity ω = { μ g / [ l ( cosθ - μ sinθ )] }1/2
Answered by Thiyagarajan K | 27 Jul, 2019, 16:53: PM

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