A small solid ball is dropped from a height above the free surface of a liquid. It strikes the surface of the liquid at $t = 0$. The density of the material of the ball is $500\ kg/m^3$ and that of liquid is $1000\ kg/m^3$ If the ball comes momeritariiy at rest at $t = 2\ sec$ then initial height of the ball from surface of liquid was ..... $m$ (neglect viscosity)
Diffcult
Download our app for free and get started
Velocity of ball when it reaches to surface of liquid
$\mathrm{a}=\frac{1000 \mathrm{gV}-500 \mathrm{gV}}{500 \mathrm{V}}$
where $V$ is the volume of the ball.
$a=10 \mathrm{m} / \mathrm{sec}^{2}$
apply $\mathrm{v}=\mathrm{u}+\mathrm{at}$
$\Rightarrow 0=\sqrt{2 g h}-10 t$
$\Rightarrow \sqrt{2 g h}=10 \times(2)$
$\Rightarrow 2 \times 10 \times h=400$
$\Rightarrow \mathrm{h}=20\, \mathrm{m}$ Ans
Download our appand 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.*
Similar Questions
- 1A light semi cylindrical gate of radius $R$ is piovted at its mid point $O$, of the diameter as shown in the figure holding liquid of density $\rho $. The force $F$ required to prevent the rotation of the gate is equal toView Solution
- 2A 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 outView Solution
- 3The terminal velocity of a copper ball of radius $2.0 \;mm$ falling through a tank of oll at $20\,^{\circ} C$ is $6.5 \;cm s ^{-1} .$ Compute the viscosity of the oil at $20\,^{\circ} C .$ Density of oil is $1.5 \times 10^{3} \;kg m ^{-3},$ density of copper is $8.9 \times 10^{3} \;kg m ^{-3}$View Solution
- 4A cylindrical tank has a hole of $1 cm^2$ in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of $70 cm^3/sec$. then the maximum height up to which water can rise in the tank is .......... $cm$View Solution
- 5The terminal velocity of a copper ball of radius $2.0 \;mm$ falling through a tank of oll at $20\,^{\circ} C$ is $6.5 \;cm s ^{-1} .$ Compute the viscosity of the oil at $20\,^{\circ} C .$ Density of oil is $1.5 \times 10^{3} \;kg m ^{-3},$ density of copper is $8.9 \times 10^{3} \;kg m ^{-3}$View Solution
- 6An ideal fluid of density $800 \; kgm ^{-3}$, flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from $a$ to $\frac{ a }{2}$. The pressure difference between the wide and narrow sections of pipe is $4100 \; Pa$. At wider section, the velocity of fluid is $\frac{\sqrt{x}}{6} \; ms ^{-1}$ for $x = \dots$ $\left(\right.$ Given $g =10 \; m ^{-2}$ )View Solution
- 7A 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 ......... $\times 10^{-6} \;m^{3} /s$View Solution
- 8A cylindrical vessel open at the top is $20$ $cm $ high and $10$ $cm$ in diameter. A circular hole whose cross-sectional area $1$ $cm^2$ is cut at the centre of the bottom of the vessel. Water flows from a tube above it into the vessel at the rate $100$ $cm^3$ $s^{^{-1}}$. The height of water in the vessel under steady state is ....... $cm$ (Take $g$ $=$ $1000 $ $cm s^{^{-2}})$View Solution
- 9A cube of edge length $10 \,cm$ is just balanced at the interface of two liquids $A$ and $B$ as shown in figure. If $A$ and $B$ has specific gravity $0.6$ and $0.4$ respectively, then mass of cube is ................ $g$View Solution
- 10The vertical limbs of a $U$ shaped tube are filled with a liquid of density $\rho$ upto a height $h$ on each side. The horizontal portion of the $U$ tube having length $2h$ contains a liquid of density $2\rho$ . The $U$ tube is moved horizontally with an accelerator $g/2$ parallel to the horizontal arm. The difference in heights in liquid levels in the two vertical limbs, at steady state will beView Solution