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2014-11-25T04:29:07+05:30

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See diagram. 
ABC is a cone of sand of base radius R and height h.  The base AB is circular.

Let us consider a point P on the slanting edge of the cone. On a small sand particle at P, there are three forces acting.  Force of friction, Normal reaction and weight.  To have the sand particle at P not to slide, we must have the forces balance each other.

       consider the force components in the horizontal direction.

               F Sin Ф = N Cos Ф,               but,    F = μ N
             μ N Sin Φ = N Cos Φ
               =>    Tan Φ = 1/μ
         But tan Φ = R / h 
         hence      h = μ R

 Maximum volume of cone = 1/3 * π R² h = π R³ μ /3

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from which syllabus is this question ? regular XI or XII class ?