A block of steel of size $5 \times 5 \times 5 \,cm ^3$ is weighed in water. If relative density of steel is $7$ , its apparent weight is ........... $g wt$
$6 \times 5 \times 5 \times 5$
$4 \times 4 \times 4 \times 7$
$5 \times 5 \times 5 \times 7$
$4 \times 4 \times 4 \times 6$
The height of water in a tank is $H$. The range of the liquid emerging out form a hole in the wall of the tank at a depth $\frac{{3H}}{4}$ from the upper surface of water, will be
Water rises to a height of $10\, cm$ in capillary tube and mercury falls to a depth of $3.1\,cm$ in the same capillary tube. If the density of mercury is $13.6$ and the angle of contact for mercury is $135^o$, the approximate ratio of surface tensions of water and mercury is
A cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with a net acceleration of $g/3$. The fraction of volume immersed in the liquid will be :-
A soap bubble in vacuum has a radius $3\, cm$ and another soap bubble in vacuum has radius $4\, cm$. If two bubbles coalesce under isothermal condition. Then the radius of the new bubble will be .............. $\mathrm{cm}$
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 fig. The lower density liquid is open to atmosphere having pressure $P_0$. Then density $D$ of solid is given by