Fine particles of a substance are to be stored in a heap on a horizontally circular plate of radius a . If the co-efficient of static friction between the particles is k, the maximum possible height of cone is :
a) ak
b) ak/2
c) a/k
d) ak2
Harshit,is the cone rotating?
well Chandni,nothing has been said about the rotation of cone.I don't have any idea about its solution.The answer given though is (d).
i got answer (a) by this logic
the outer layer of particles will be protected from sliding by the inner layer if k>=tanø (using the concept of angle of repose)
where ø is the angle between radius and slant height
so k>=h/a
h<=ak
so maximum value of h=ak
please tell if this solution is right?
Harshit,I don't think it is correct because outer particles experience normal reaction by other particles then it is along the slant height of the cone.If the angle between the slant height and the radius is phi then Nsin(phi)=[dm]g where dm is the mass of an elementary layer.f=Ncos(phi).f<=kN.After doing calculations,k>=a/{a^2 +h^2}.
Yes Harshit it should be ak as tan ø=k and for h to be maximum static friction should be maximum.
tan ø=k = h/a
Looks like inclined plane situation.
The component of gravity is balanced by frictional force.mgsin(theta)=kmgcos(theta)==>tan(theta)=k and tan(theta)=h/a.Hence ,h=ak.