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Mechanics

Hot goIITian

 Joined: 24 Jun 2012 Post: 177
12 Jul 2012 21:41:07 IST
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a particle is placed at rest inside a hollow hemisphere of radius "R". the coefficient of friction between the particle and hemisphere is 1/root3 .the maximum height upto which particle can remain stationary?

plz give steps

Blazing goIITian

Joined: 8 Oct 2008
Posts: 8064
31 Jul 2012 16:58:07 IST
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hello,

let it be h from top.now makes the f.b.d. of particle and let the angle between normal (exerted by hemisphere) and vertical be .

then-n=mgcos.................eq.1

f=mgsin=========>1/root 3 n=mgsin...........eq.2

dividing eq.2 and eq.1.............

1\root3=tan============>=30 degree

hence cos=h/r======>r*root3/2=h and hence from ground height is r-h=r-r*root3/2 ans.

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