Which of the following functions of $A$ and $B$ may be performed if $A$ and $B$ possess different dimensions
$\frac{A}{B}$
$A + B$
$A -B$
none
A homogeneous solid cylinder of length $L(L < H/2)$, cross-sectional area $A/5$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $L/4$ in the denser liquid as shown in the figure. The lower density liquid is open to atmosphere having pressure $P_0$. Then, density $D$ of solid is given by
The work done in blowing a soap bubble of radius $0.2\,m$, given that the surface tension of soap solution is $60\times10^{-3}\, N/M$ is
A wooden block with a coin placed on its top floats in water as shown in figure. $l$ and $h$ are as shown. After some time the coin falls into the water then
A liquid $X$ of density $3.36\, g/cm^3$ is poured in a $U$ -tube upto $10\, cm$ height, which contains $Hg.$ Another liquid $Y$ is poured in left arm with height $8\, cm$. Upper levels of $X$ and $Y$ are same. ............ $gm/cc$ is density of $Y$ .
(Density of $Hg = 13.6 \times 10^3\, kg/m^3$)
A wooden cube first floats inside water when a $200\,g$ mass is placed on it. When the mass is removed the cube is $2\,cm$ above water level. The side of cube is ......... $cm$