A worker wishes to pile a cone of sand onto a circular area in his yard. The radius of the circle is r,and no sand is to spill on to the surrounding area. If `mu` is the static coefficient of friction between each layer of sand along the slope and the sand, show that the greatest volume of sand that can be stored in this manner is `(1)/(3) pi muR^(3)`.

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)

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 of sand on sand,the sand pile . Density of sand =rho

Sand is piled up on a horizontal ground in the form of a regualr cone of a fixed base of radius R .The coefficient of static friction between sand layers is mu .The maximum volume of sand that can be piled up, without the sand slipping on the surface is

The figure below shows a block of mass M connected to an ideal string which passes through a thin fixed smooth pipe. On the other end, a particle of mass m is connected which revolves in a vertical circle of radius r. If the coefficient of friction between M and the surface is mu = 2/3 , then for what minimum value of M, the block of mass m can undergo complete vertical circular motion?

The radius of the base of a right circular cone of semi-vertical angle alpha is r .Show that its volume is (1)/(3)pi r^(3) cot alpha and curved surface area is pi r^(2) coses alpha.

When an object moves through a fluid, as when a ball falls through air or a glass sphere falls through water te fluid exerts a viscous foce F on the object this force tends to slow the object for a small sphere of radius r moving is given by stoke's law, F_(w)=6pietarv . in this formula eta in the coefficient of viscosity of the fluid which is the proportionality constant that determines how much tangential force is required to move a fluid layer at a constant speed v, when the layer has an area A and is located a perpendicular distance z from and immobile surface. the magnitude of the force is given by F=etaAv//z . For a viscous fluid to move from location 2 to location 1 along 2 must exceed that at location 1, poiseuilles's law given the volumes flow rate Q that results from such a pressure difference P_(2)-P_(1) . The flow rate of expressed by the formula Q=(piR^(4)(P_(2)-P_(1)))/(8etaL) poiseuille's law remains valid as long as the fluid flow is laminar. For a sfficiently high speed however the flow becomes turbulent flow is laminar as long as the reynolds number is less than approximately 2000. This number is given by the formula R_(e)=(2overline(v)rhoR)/(eta) In which overline(v) is the average speed rho is the density eta is the coefficient of viscosity of the fluid and R is the radius of the pipe. Take the density of water to be rho=1000kg//m^(3) Q. Blood vessel is 0.10 m in length and has a radius of 1.5xx10^(-2) m blood flows at rate of 10^(-7)m^(3)//s through this vessel. The pressure difference that must be maintained in this flow between the two ends of the vessel is 20 Pa what is the viscosity sufficient of blood?