Q. A cube of ice of edge 4cm is placed in an empty cylindrical glass of initial diameter 6 cm. Assume that the ice melts uniformly from each side so that it always retains its cubical shape. Remembering that ice is lighter than water, find the length of the edge of the ice cube at the instant it just leaves contact with the bottom of the glass.
1solution can be obtained by considering these to equations ...
let the final length of each side be x cm
h be the ht. of water in the container ...
Ï is the density of ice which is a known quantity ..
according to the floatation law ..
x3Ï = 1*x2h ... eq 1
quantity of water melted ....
Ï€r2h - x2h = 43 - x3 .. eq 2
and finally we get the equation ...
Ï€r2Ïx - x3Ï = 43 - x3
put the values and get the solution .... :)
106@ankit .. can u explain ur steps to mee .. i cudnt get anything.. :(
1
the ice will not lift up untill the the upthrust due to displaced water is equal to the wt. of ice ..
the LHS of the 1st eq is the total wt. of final ice
the RHS of the 1st eq is the total wt. of water displaced by it ...
according to the question just after this pt the ice can go up ...
the LHS of the 2nd eq is the volume of water in the container which is equal to the volume of ice melted ...