A hollow sphere of radius $R$ is filled completely with an ideal liquid of density $\rho$. sphere is moving horizontally with an acceleration $2g,$ where $g$ is acceleration due to gravity in the space. If minimum pressure of liquid is $P_0$, then pressure at the centre of sphere is
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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 $h$ . The incorrect statement is
A stone is projected vertically up from the bottom of a water tank. Assuming no water resistance it will go up and come down in same time but if water drag is present then the time it takes to go up, $t_{up}$ and the time it takes to come down, $t_{down}$ are related as
A hot air balloon is carrying some passengers, and a few sandbags of mass $1 kg$ each so that its total mass is $480 kg$. Its effective volume giving the balloon its buoyancy is $V$. The balloon is floating at an equilibrium height of $100 m$. When $N$ number of sandbags are thrown out, the balloon rises to a new equilibrium height close to $150 m$ with its volume $V$ remaining unchanged. If the variation of the density of air with height $h$ from the ground is $\rho(h)=\rho_0 e^{-\frac{h}{h_0}}$, where $\rho_0=1.25 kg m ^{-3}$ and $h _0=6000 m$, the value of $N$ is. . . . .
A boy has $60\, kg$ weight. He wants to swim in a river with the help of a wooden log. If relative density of wood is $0.6$, what is the minimum volume of wooden log? (density of river water is $1000\, kg/m^3$)
$Assertion :$ The buoyant force on a submerged rigid object can be considered to be acting at the centre of mass of the object.
$Reason :$ For a rigid body a force field distributed uniformly through its volume can be considered to be acting at the centre of mass of the body.
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 ball of relative density $0.8$ falls into water from a height of $2$ $m$. The depth to which the ball will sink is ........ $ m$ (neglect viscous forces) :
A submarine experiences a pressure of $5.05\times 10^6\,Pa$ at a depth of $d_1$ in a sea. When it goes further to a depth of $d_2,$ it experiences a pressure of $8.08\times 10^6\,Pa.$ Then $d_2 -d_1$ is approximately ........ $m$ (density of water $= 10^3\,kg/m^3$ and acceleration due to gravity $= 10\,ms^{-2}$ )