A cylinder containing water up to a height of $25 cm$ has a hole of cross-section $\frac{1}{4}c{m^2}$ in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out
AIncrease of $12.5 gm-wt$
BIncrease of $ 6.25 gm-wt$
CDecrease of $12.5 gm-wt$
DDecrease of $ 6.25 gm-wt$
Diffcult
Download our app for free and get started
CDecrease of $12.5 gm-wt$
c (c)Let $ A =$ The area of cross section of the hole
$v =$ Initial velocity of efflux
$d = $ Density of water,
Initial volume of water flowing out per second $ = Av$
Initial mass of water flowing out per second $ = Avd$
Rate of change of momentum $= Adv2$
Initial downward force on the flowing out water $= Adv2$
So equal amount of reaction acts upwards on the cylinder.
Initial upward reaction =$Ad{v^2}$ [As $v = \sqrt {2gh} $]
$\therefore $ Initial decrease in weight $ = Ad\,(2gh)$
$ = 2Adgh$$ = 2 \times \left( {\frac{1}{4}} \right) \times 1 \times 980 \times 25 = 12.5$ $gm-wt.$
Download our app
and get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
A piece of copper having an internal cavity weights $264\, g$ in air and $221\, g$ in water. Find volume (in $cc$) of cavity. Density of $Cu = 8.8\, g/cc$
Two liquids of densities $d_1$ and $d_2$ are flowing in identical capillary tubes uder the same pressure difference. Ift $t_1$ and $t_2$ are time taken for the flow of equal quantities (mass) of liquids, then the ratio of coefficient of viscosity of liquids must be
A plane is in level flight at constant speed and each of its two wings has an area of $40 \mathrm{~m}^2$. If the speed of the air is $180 \mathrm{~km} / \mathrm{h}$ over the lower wing surface and $252 \mathrm{~km} / \mathrm{h}$ over the upper wing surface, the mass of the plane is______ $\mathrm{kg}$. (Take air density to be $1 \mathrm{~kg} \mathrm{~m}^{-3}$ and $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )
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?
A small hole of area of cross-section $2\; \mathrm{mm}^{2}$ is present near the bottom of a fully filled open tank of height $2\; \mathrm{m} .$ Taking $\mathrm{g}=10 \;\mathrm{m} / \mathrm{s}^{2},$ the rate of flow of water through the open hole would be nearly ......... $\times 10^{-6} \;m^{3} /s$
Two different liquids are flowing in two tubes of equal radius. The ratio of coefficients of viscosity of liquids is $52:49$ and the ratio of their densities is $13:1$, then the ratio of their critical velocities will be