A worker wishes to pile up sand on to a circular area of radius `R`. No sand is to spill on to the surrounding area. If `mu_(s)` is the coefficient of static friction sand particles, then choose the correct statement (s)

Options

A. The greatest height of sand pile that can be created is `mu_(s)R`.
B. The greatest height of sand pile that can be created is `R//mu_(s)`
C. Minimum work required to create greatest height sand pile is `(pi)/12 mu_(s)^(2)R^(4) rho g`. Where `rho` is the density of sand volume
D. Sand pile will be in stable equilibrium

Answer

A, C

Explanation

From free body diagram of sand particle
`tantheta=mu s =h/R`
work required `=(1/3 pi R^(2)h rhog)h/4`
The system is in unstable equilibrium.