Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes $0.01 \,cm ^{3}$ of oleic acid per $cm ^{3}$ of the solution. Then you make a thin film of this solution (monomolecular thickness) of area $4\, cm ^{2}$ by considering $100$ spherical drops of radius $\left(\frac{3}{40 \pi}\right)^{\frac{1}{3}} \times 10^{-3}\, cm .$ Then the thickness of oleic acid layer will be $x \times 10^{-14} \,m$. Where $x$ is ...... .
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In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are $70 \;m s ^{-1}$ and $63\; m s ^{-1}$ respectively. What is the lift on the wing if its area is $2.5 \;m ^{2}$ ? Take the density of atr to be $1.3\; kg m ^{-3} .$
Rank in order, from highest to lowest, the liquid heights $h_a$ to $h_d$ .The air flow is from left to right. The liquid columns are not drawn to scale
Two cylindrical vessels of equal cross-sectional area $16\,cm ^{2}$ contain water upto herghts $100\,cm$ and $150\,cm$ respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is $......J$ [Take density of water $=10^{3}\,kg / m ^{3}$ and $g =10\,ms ^{-2}$ ]
Consider the wall of a dam to be straight with height $H$ and length $L$. It holds a lake of water of height $h (h < H)$ on one side. Let the density of water be $\rho_{ w }$. Denote the torque about the axis along the bottom length of the wall by $\tau_1$. Denote also a similar torque due to the water up to height $h / 2$ and wall length $L / 2$ by $\tau_2$. Then $\tau_1 / \tau_2$ (ignore atmospheric pressure) is
Assume that, the drag force on a football depends only on the density of the air, velocity of the ball and the cross-sectional area of the ball. Balls of different sizes but the same density are dropped in an air column. The terminal velocity reached by balls of masses $250 \,g$ and $125 \,g$ are in the ratio
A certain block weight $15\, N$ in air. It weight $12\, N$ when immersed in water when immersed in another liquid it weighs $13\, N$, the relative density of the block is
The 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 be
A spring balance reads $200 \,gF$ when carrying a lump of lead in air. If the lead is now immersed with half of its volume in brine solution, what will be the new reading of the spring balance? specific gravity of lead and brine are $11.4$ and $1.1$ respectively ........... $gF$