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A liquid flows through a horizontal tube. The velocities of the liquid in the two sections, which have areas of cross-section ${A_1}$ and ${A_2}$, are ${v_1}$ and ${v_2}$ respectively. The difference in the levels of the liquid in the two vertical tubes is $ h$
A fire hydrant delivers water of density $\rho $ at a volume rate $L$. The water travels vertically upward through the hydrant and then does $90^o$ turn to emerge horizontally at speed $V$. The pipe and nozzle have uniform cross-section throughout. The force exerted by the water on the corner of the hydrant is
A small ball of mass $M$ and density $\rho$ is dropped in a viscous liquid of density $\rho_0$. After some time, the ball falls with a constant velocity. What is the viscous force on the ball ?
Different physical quantities are given in Column - $\mathrm{I}$ and their dimensional formula are given in Column - $\mathrm{II}$. Match them appropriately.
A load of mass $M\,kg$ is suspended from a steel wire of length $2\,m$ and radius $1.0\,mm$ in Searle’s apparatus experiment. The increase in length produced in the wire is $4.0\,mm.$ Now the load is fully immersed in a liquid of relative density $2$. The relative density of the material of load is $8$. The new value of increase in length of the steel wire is ........ $mm$
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 $g =10\,ms ^{-2}$ ]
A beaker containing water is placed on the platform of a spring balance. The balance reads $1.5$ $kg$. A stone of mass $0.5$ $kg$ and density $500$ $kg/m^3$ is immersed in water without touching the walls of beaker. What will be the balance reading now ? ..... $kg$
An incompressible fluid flows steadily through a cylindrical pipe which has radius $2r$ at point $A $ and radius $r $ at $B $ further along the flow direction. If the velocity at point $A$ is $v, $ its velocity at point $B$ is
A liquid of mass $1$ $kg$ is filled in a flask as shown in figure. The force exerted by the flask on the liquid is $(g = 10\ m/s^2)$[Neglect atmospheric pressure]: