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A hollow sphere of volume $V$ is floating on water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water
A spherical ball of density $\rho$ and radius $0.003$ $m$ is dropped into a tube containing a viscous fluid filled up to the $0$ $ cm$ mark as shown in the figure. Viscosity of the fluid $=$ $1.260$ $N.m^{-2}$ and its density $\rho_L=\rho/2$ $=$ $1260$ $kg.m^{-3}$. Assume the ball reaches a terminal speed by the $10$ $cm$ mark. The time taken by the ball to traverse the distance between the $10$ $cm$ and $20$ $cm$ mark is
( $g$ $ =$ acceleration due to gravity $= 10$ $ ms^{^{-2}} )$
A metal block of base area $0.20\,m ^2$ is placed on a table, as shown in figure. A liquid film of thickness $0.25\,mm$ is inserted between the block and the table. The block is pushed by a horizontal force of $0.1\,N$ and moves with a constant speed. If the viscosity of the liquid is $5.0 \times 10^{-3} \;Pa-s$, the speed of block is $.........\times 10^{-3}\,m / s$
$10,000 $ small balls, each weighing $1\, gm$, strike one square cm of area per second with a velocity $100 \,m/s$ in a normal direction and rebound with the same velocity. The value of pressure on the surface will be
Equal volumes of two immiscible liquids of densities $\rho$ and $2\rho$ are filled in a vessel as shown in figure. Two small holes are punched at depth $h/ 2$ and $3h/2$ from the surface of lighter liquid. If $v_1 $ and $v_2 $ are the velocities of a flux at these two holes, then $v_1/v_2 $ is :
Two solid spheres $A$ and $B$ of equal volumes but of different densities $d_A$ and $d_B$ are connected by a string. They are fully immersed in a fluid of density $d_F$. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if
What will be the nature of flow of water from a circular tap, when its flow rate increased from $0.18\, L / min$ to $0.48\, L / min$ ? The radius of the tap and viscosity of water are $0.5\, cm$ and $10^{-3}\, Pa s$, respectively.
A $0.5\ kg$ mass of lead is submerged in a container filled to the brim with water and a block of wood floats on top. The lead mass is slowly lifted from the container by a thin wire and as it emerges into air the level of the water in the container drops a bit. The lead mass is now placed on the block of wood. As the lead is placed on the wood.
A wide vessel with a small hole at the bottom is filled with two liquids. The density and heightof one liquid are $\rho_1$ and $h_1$ and that of the otherare $\rho_2$ and $h_2 \ (\rho_1 >\rho_2)$. The velocity of liquid coming out of the hole is :