Sand 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 . Maximum volume of the sand can be piled up in the form of cone without slipping on the ground is

Step-by-step solution

Let h= critical height of sand cone of radius R . Then, for a sand particle to be in equilibrium (it must no slips to the ground) aligned & f =N & where, f= friction, & & N= normal reaction and f= N & N =N & = 1 = R h (from figure) aligned So, maximum volume of sand cone that can be formed over level ground is V_ = 1 3 R^2 h= 1 3 R^2( R)= R^3 3