Embibe Experts Solutions for Exercise 7: Assignment

A capillary tube of length $10 \mathrm{cm}$ is dipped $3 \mathrm{cm}$ inside water. The water rises up to $5 \mathrm{cm}$ in the capillary. If the same tube is dipped $6 \mathrm{cm}$ inside water, the water will rise in capillary up to height _____ $\mathrm{cm}.$

A block of mass $1 \mathrm{kg}$ and relative density $0.8$ is immersed in water and fastened to bottom as shown in figure. If the tank is accelerated upward with $1 \mathrm{m} {\mathrm{s}}^{–2}$, then tension in the string is _____ $\mathrm{N}.$ $\left(g=10 \mathrm{m} {\mathrm{s}}^{–2}\right)$

A tank of area $A$ is filled with two immiscible liquids of density $2\rho$ and $\rho$ with height $h$ and $2h$ respectively as shown in figure. If a small orifice of area $a$ is made near bottom, the total time required to empty the tank is $\frac{kA}{a}\sqrt{\frac{h}{g}}\left(2-\frac{1}{\sqrt{2}}\right)$, the value of $k$ is _____.

Consider a liquid (density $d$) column of height $h$ contained in a cylinder of cross section area $A.$ There is a piston of mass $m$ above the liquid as shown. If $\frac{mg}{A}=p_0$ ($p_0=$atmospheric pressure) and $p_0=hdg$, then velocity of efflux from the narrow hole at bottom, is $N\sqrt{\frac{p_0}{d}}$, the value of $N$ is _____.

Vessel is accelerated vertically upward with acceleration $a=10 \mathrm{m} {\mathrm{s}}^{–2}.$ If value of $\left|P_B-P_A\right|$ is $N\rho H$, then the value of $N$ is _____.

A container is accelerating with acceleration $a=g$ along the direction as shown below. The angle $\theta$ (in degree) made by the liquid surface with the vertical wall of the container, is _____.

A soap film is formed on a triangular wire frame having two fixed and one movable side. The free side is moved with a constant acceleration $\text{'}a\text{'}.$ Take side length to be zero at $t=0$ as shown. If the surface tension is constant and $U$ is the surface potential energy of the soap film then $\frac{dU}{dt}\propto t^N$, the value of $N$ is _____.

A solid cylinder of length $l$ is in equilibrium in two different liquids $A$ and $B$ as shown in the figure. If density of the cylinder is $\frac{P}{Q}\rho$, then value of $\left(P+Q\right)$ is $P$ and $Q$ are co-prime numbers) (Density of liquid $A=\rho$ and density of liquid $B=3\rho$)