Embibe Experts Solutions for Exercise 7: Assignment

A sphere of radius $r$ is dropped in a liquid from its surface. Which of the following graphs is/are correct?

A cone of radius $R$ and height $H$, is hanging inside a liquid of density $\rho$ by means of a string as shown in the figure. If ratio of the force acting on the slant surface to that on the base by the liquid is $P : Q$ then value of $\left(P+Q\right)$ is _____. (Assume atmospheric pressure is zero and vertex of cone is just touching the liquid surface)

Four spheres of equal radii $R$ are arranged as shown in figure. All four spheres are in equilibrium. Given that ${\rho }_A=2\rho , {\rho }_B=4\rho , {\rho }_D=5\rho$ and spring constant $=k.$ If elongation produced in the spring is $\frac{N\pi \rho R^{3}g}{3k}$ then $N$ is _____.

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 _____ $\mathrm{N}.$ $\left(g=10 \mathrm{m} {\mathrm{s}}^{–2}\right)$

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 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 $B=3\rho$)