IIT JEE , AIEEE Forum - Physics , Mechanics

kghedriu

let the coeficient of friction be 'k' and 'w' be the angular speed...instead of theta, i am using @.....

well....as friction acts along the tangent to the sphere....u get the range of w wen u vary the direction of fricition....and well.....resolve the forces carefully...and u get the equations as:

kg cos@ + k r sin@ w^2 sin@ + r sin@ w^2 cos@= g sin @

so, w= [g (sin@-kcos@) /r sin@(cos@+k sin@)]^1/2-------------(1)

similarly take the friction to b downwards..u get

w= [g(sin @ +k cos@)/r sin@( cos@ - k sin@)]^1/2----------(2)

hence the range is between the equations (1) and (2)

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