An inverted cone of height `H`, and radius `R` is pointed at bottom. It is completely filled with a volatile liquid. If the rate of evaporation is directly proportional to the surface area of the liquid in contact with air (constant of proportionality k `gt` 0). Find the time in which whole liquid evaporates.

A right circular cone with radius R and height H contains a liquid which evaporates at a rate proportional to its surface area in contact with air (proportionality constant k is positive). suppose that r(t) is the radius of the liquid cone at time t.The radius of water cone at t=1 is

A right circular cone with radius R and height H contains a liquid which evaporates at a rate proportional to its surface area in contact with air (proportionality constant k is positive). suppose that r(t) is the radius of the liquid cone at time t.The time after which the cone is empty is

spherical rain drop evaporates at a rate proportional to its surface area.The differential equation corresponding to the rate of change of the radius of the rain drop if the constant of proportionality is K>0 is

A solid cone of height H and base radius H/2 floats in a liquid of density rho . It is hanging from the ceiling with the help of a string. The force by the fluid on the curved surface of the cone is ( P_(0) = atmospheric pressure)

A circular cylinder of height h_(0)=10 cm and radius r_(0) =2 cm is opened at the top and filled with liquid. It is rotated about its vertical axis. Determine the speed of rotation so that half the area of the bottom gets exposed ( g=10 m//s^(2) ):

Spirit in a bowl evaporates at a rate that is proportional to the surface area of the liquid. Initially, the height of liquid in the bowl is H_(0) . It becomes (H_(0))/(2) in time t_(0) . How much more time will be needed for the height of liquid to become (H_(0))/(4)

A stream line body with relative density rho_(1) falls into air from a height h_(1) on the surface of a liquid of realtive density rho_(2) , where rho_(2) gt rho_(1) . Find the time of immersion of the body into the liquid.

A cylindrical container of radius 'R' and height 'h' is completely filled with a liquid. Two horizontal L -shaped pipes of small cross-sectional area 'a' are connected to the cylinder as shown in the figure. Now the two pipes are opened and fluid starts coming out of the pipes horizontally in opposite directions. Then the torque due to ejected liquid on the system is