Figure below shows a liquid being pushed out of the tube by a piston having area of cross section $2.0\,cm ^2$. The area of cross section at the outlet is $10\,mm ^2$. If the piston is pushed at a speed of $4\,cm s ^{-1}$, the speed of outgoing fluidis $.........\,cm s ^{-1}$.
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A metallic body of material with density of $8000\ kg/m^3$ has a cavity inside. A spring balance shows its mass to be $10.0\ kg$ in air and $7.5\ kg$ when immersed in water. The ratio of the volume of the cavity to the volume of the material of the body must be
A drinking straw is dipped in a pan of water to depth d from the surface (see figure below). Now water is sucked into it up to an initial height $h_0$ and then left to oscillate. As a result, its height $y$ from the surface of the water varies periodically. Ignoring damping, the equation for $y$ is ( $g$ is the acceleration due to gravity):
A liquid flows in the tube from left to right as shown in figure. $A_1$ and $A_2$ are the cross-sections of the portions of the tube as shown. The ratio of speed $\frac{v_1}{v_2}$ will be ..........
A metal block of base area $0.2\; m ^{2}$ is connected to a $0.02\; kg$ mass via a string that passes over an ideal pulley as shown in figure. A liquid film of thickness $0.6\; mm$ is placed between the block and the table. When released the block moves to the right with a constant speed of $0.17\; m / s$. The co-efficient of viscosity of the liquid is
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
Water is moving with a speed of $5.18 ms^{-1}$ through a pipe with a cross-sectional area of $4.20 cm^2$. The water gradually descends $ 9.66 m $ as the pipe increase in area to $7.60 cm^2$. The speed of flow at the lower level is ....... $ms^{-1}$
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 $g =10\,ms ^{-2}$ ]