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  • A block of mass m is kept on the edge of the horizontal turn table of radius R  Turn table is rotating with constant angular velocity w . coefficient of friction is <img alt="\m

A block of mass m is kept on the edge of the horizontal turn table of radius R 

Turn table is rotating with constant angular velocity w . coefficient of friction is \mu . If the block is

just about to move find angular velocity w of the turn table 

 

Option: 1

\sqrt{\frac{\mu g}{R}}


Option: 2

\sqrt{\frac{\mu }{Rg}}


Option: 3

\sqrt{\frac{\mu }{R}}


Option: 4

\sqrt{\frac{R}{\mu g }}


Answers (1)

As we have learned

Skidding of object on a Rotating Platform -

Centripetal force \leq Force of friction

m\omega^{2}r\leq\mu mg

\therefore\ \omega_{max}=\sqrt{(\mu g/r)}

\omega=Angular velocity

r = radius

\mu= coefficient of friction

- wherein

It is the maximum velocity of rotation of the platform, so that object will not skid on it.

 

 Centrifugal force on the block 

F _c= mw^2 R

f _s= mw^2 R

for limiting case 

f _s=f_L = \mu N = \mu mg

centripetal force will be provided by limiting frictional force 

So \mu mg = mw^2 R \Rightarrow w = \sqrt{\frac{\mu g}{R}}

 

 

 

 

Posted by

Sumit Saini

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