An open-ended $U$-tube of uniform cross-sectional area contains water (density $1.0 $ gram/centimeter$^3$) standing initially $20$ centimeters from the bottom in each arm. An immiscible liquid of density $4.0$ grams/ centimeter $^3$ is added to one arm until a layer $5$ centimeters high forms, as shown in the figure above. What is the ratio $h_2/h_1$ of the heights of the liquid in the two arms?
$3/1$
$5/2$
$2/1$
$3/2$
Two bodies having volumes $V$ and $2V $ are suspended from the two arms of a common balance and they are found to balance each other. If larger body is immersed in oil (density $d_1 $ $=$ $ 0.9$ $ gm/cm^3$) and the smaller body is immersed in an unknown liquid, then the balance remain in equilibrium. The density of unknown liquid is given by ......... $gm/cm^3$
A $U$ tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of $10\,\, mm$ above the water level on the other side. Meanwhile the water rises by $65\,\, mm$ from its original level (see diagram). The density of the oil is ......... $kg/m^3$
A cylindrical vessel of base radius $R$ and height $H$ has a narrow neck of height $h$ and radius $r$ at one end (see figure). The vessel is filled with water (density $\rho_w$ ) and its neck is filled with immiscible oil (density $\rho_0$ ). Then, the pressure at
The atmospheric pressure and height of barometer column is $10^5\,Pa$ and $760\,mm$ respectively on the Earth surface. If the barometer is taken to the Moon then column height will be ........ $mm$
An aeroplane of mass $3 \times 10^4\,kg$ and total wing area of $120\,m^2$ is in a level flight at some height. The difference in pressure between the upper and lower surfaces of its wings in kilopascals is........... $kPa$ $(g=10\,m/s^2)$