A wooden cylinder floats vertically in water with half of its length immersed. The density of wood is
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(b) $V\rho g = \frac{V}{2}\sigma g$
$\rho = \frac{\sigma }{2}$ ($\sigma$ = density of water)
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A wooden block floats in a liquid with $40\%$ of its volume inside the liquid. When the vessel containing he liquid starts rising upwards with acceleration $a = g/2$, the percentage of volume inside the liquid is ......... $\%$
We have two (narrow) capillary tubes $T_1$ and $T_2$. Their lengths are $l_1$ and $l_2$ and radii of cross-section are $r_1$ and $r_2$ respectively. The rate of flow of water under a pressure difference $ P$ through tube $T_1$ is $8cm ^3/sec$. If $l_1 = 2l_2$ and $ r_1 =r_2$, what will be the rate of flow when the two tubes are connected in series and pressure difference across the combination is same as before $ (= P)$
A vertical U-tube of uniform cross-section contains water in both the arms. A $10 \,cm$ glycerine column ($R.D$. $=1.2$ ) is added to one of the limbs. The level difference between the two free surfaces in the two limbs will be ...... $cm$
If solid will break under pressure greater than $13\ atm$ and that solid has a specific gravity of $4$ , what is the maximum height of a cylinder made from the solid that can be built at the earth's surface ? (Note: $1\ atm$ = $10^5\ Pa$ .) ......... $m$
Consider a water tank as shown in the figure. It's cross-sectional area is $0.4\, m ^{2}$. The tank has an opening $B$ near the bottom whose cross-section area is $1\, cm ^{2}$. A load of $24\, kg$ is applied on the water at the top when the height of the water level is $40\, cm$ above the bottom, the velocity of water coming out the opening $B$ is $v\, ms ^{-1}$. The value of $v$, to the nearest integer, is ......$m/s$. [Take value of $g$ to be $10 \,ms ^{-2}$ ]
The two thigh bones (femurs), each of cross-sectional area $10\; cm ^{2}$ support the upper part of a human body of mass $40\; kg$. Estimate the average pressure sustained by the femurs.
Three identical vessels are filled to the same height with three different liquids $A, B$ and $C$ $({\rho _A} > {\rho _B} > {\rho _C})$. The pressure at the base will be
A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of $10 \mathrm{~N}$ is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is_________.${N}$.
The density of the atmosphere at sea level is $1.29 \;kg / m ^{3} .$ Assume that it does not change with altitude. Then how high (in $km$) would the atmosphere extend?