A cork is submerged in water by a spring attached to the bottom of a bowl. When the bowl is kept in an elevator moving with acceleration downwards, the length of spring
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(b) Effective weight $W' = m(g - a)$ which is less than actual weight $mg,$ so the length of spring decreases.
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$9\ kg$ of mercury is poured into a glass $U-tube$ with inner diameter of $1.2 \ cm$. The mercury can flow without friction within the tube. the oscillation period ......... $\sec$. Density of mercury = $13.6 × 10^3\ kg/m^3$.
The Pitot tube shown in the figure is used to measure fluid flow velocity in a pipe of cross sectional area $S$. It was invented by a French engineer Henri Pitot in the early $18^{th}$ century. The volume of the gas flowing across the section of the pipe per unit time is (The difference in the liquid columns is $\Delta h, \rho_0$ and $\rho$ are the densities of liquid and the gas respectively) :-
Water is flowing through a channel (lying in a vertical plane) as shown in the figure. Three sections $A, B$ and $C$ are shown. Sections $B$ and $C$ have equal area of cross section. If $P_A, P_B$ and $P_C$ are the pressures at $A, B$ and $C$ respectively then
A cylindrical vessel filled with water is released on an inclined surface of angle $\theta$ as shown in figure.The friction coefficient of surface with vessel is $\mu( < \tan \theta)$.Then the contact angle made by the surface of water with the incline will be
A log of wood of mass $120 Kg$ floats in water. The weight that can be put on the raft to make it just sink, should be ....... $Kg$ (density of wood = $600 Kg/m^3$)
There is a $1\, mm$ thick layer of glycerine between a flat plate of area $100\, cm^2$ and a big plate. If the coefficient of viscosity of glycerine is $1.0\, kg\, (m-s)$, then ....... $N$ force is required to move the plate with a velocity of $7\, cm/s$ .
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