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S and is to be piled up on a horizontal ground in the form of a regular cone of a fixed base of radius R. Coefficient of static friction between the sand layers is mu. Maximum volume of the sand can be piled up in the form of cone without slipping on the ground is |
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Answer» `(mu R^(3))/(3 pi)`  `f sin phi = N COS phi` where, f= friction. N = normal reaction and `f= muN` `rArr""mu N sin phi = N cos phi` `rArr" "tan phi =(1)/(mu) =(R)/(h)` (from figure) So, maximum VOLUME of sand cone that can be formed over level ground is `V_("max") =(1)/(3) pi R^(2) h =(1)/(3) pi R^(2) (mu R) =(mu pi R^(3))/(3)` |
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