A pressure-pump has a horizontal tube of cross-sectional area $10\,cm ^{2}$ for the outflow of water at a speed of $20\,m / s$. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is $...N$ [given : density of water $=1000\,kg / m ^{3}$ ]
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A solid sphere of density $\eta$ $( > 1)$ times lighter than water is suspended in a water tank by a string tied to its base as shown in fig. If the mass of the sphere is m then the tension in the string is given by
$Assertion :$ Falling raindrops acquire a terminal velocity.
$Reason :$ A constant force in the direction of motion and a velocity dependent force opposite to the direction of motion, always result in the acquisition of terminal velocity.
A liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base. If the radius of the vessel is $ r $ and angular velocity of rotation is $\omega $, then the difference in the heights of the liquid at the centre of the vessel and the edge is
Consider the configuration of a stationary water tank of cross-section area $A_{0}$ and a small bucket as shown in figure below; the speed $v$ is .......... $m/s$ of the bucket, so that the water leaking out of a hole of cross-section area $A$ (as shown) from the water tank does not fall outside the bucket? (Take, $h=5 \,m , H=5 \,m , g=10 \,m / s ^{2}, A=5 \,cm ^{2}$ and $\left.A_{0}=500 \,cm ^{2}\right)$.
A small spherical ball of radius $r$, falling through a viscous medium of negligible density has terminal velocity ' $v$ '. Another ball of the same mass but of radius $2 r$, falling through the same viscous medium will have terminal velocity:
Air streams horizontally past an air plane. The speed over the top surface is $60 \,m / s$ and that under the bottom surface is $45 \,m / s$. The density of air is $1.293 \,kg / m ^3$, then the difference in pressure is ....... $N / m ^2$
A cube of external dimension $10\ cm$ has an inner cubical portion of side $5\ cm$ whose density is twice that of the outer portion. If this cube is just floating in a liquid of density $2\ g/cm^3$, find the density of the inner portion