A $U-$ tube in which the cross-sectional area of the limb on the left is one quarter, the limb on the right contains mercury (density $13.6\ g/cm^3$). The level of mercury in the narrow limb is at a distance of $36\ cm$ from the upper end of the tube. What will be the rise in the level of mercury in the right limb if the left limb is filled to the top with water ....... $cm$

- A
$1.2$

- B
$2.35$

- C
$0.56$

- D
$0.8$

If the terminal speed of a sphere of gold (density $= 19.5\, kg/m^3$) is $0.2\, m/s$ in a viscous liquid (density $= 1.5\, kg/m^3$), find the terminal speed of a sphere of silver (density $=10.5\, kg/m^3$) of the same size in the same liquid ........ $m/s$

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 :-

In a $U-$ tube experiment, a column $AB$ of water is balanced by a column $‘CD’$ of oil, as shown in the figure. Then the relative density of oil is

The excess pressure inside the first soap bubble is three times that inside the second bubble then, the ratio of volume of the first to the second bubble will be

Which of the following functions of $A$ and $B$ may be performed if $A$ and $B$ possess different dimensions