Question

1)A vessel contains oil (density 0.8 g/cc) over Mercury( density 13.6 g/cc).a homogeneous sphere floats with half its volume immersed in Mercury and the othe half in the oil .the density of the material of the sphere in g/cc is.

2) the density of ice is Y gram/litre and that of water is X gram/litre. what is the change in volume when M gram of ice melts.

Answer 1

1.
The total weight is balanced by the displaced volumess of the two different fluids. Let it,s Vol is V and the density is n. Then the equilibrium condition should be

Vng=V/2*(0.8)g+V/2*(13.6)g
or n=0.4+6.8=7.2 gm/cc


2.
Initial volume = Initial mass/Initial density = m/y ---(i)
Final volume = Final mass/Final density ---(ii)
Change in volume = Final volume - Initial volume
OR m/x - m/y
OR m[(1/x) - (1/y)]
Change in volume = m[(1/x) -(1/y)]