Archimedes' Principle and Buoyancy

Two cubical blocks of same dimensions but masses $m$ and $3 m$ are joined by a string and are at equilibrium in water as shown in figure. Then

Let $T$ represent the true weight of a body, $B$ the force of buoyancy on the body when immersed in a liquid, $A$ represents the apparent weight of the body and $W$ be twice the weight of liquid displaced by the body. Then which of the following relation is correct?

A cubical block of wood having an edge $10 \mathrm{cm}$ and mass $0.92 \mathrm{kg}$ floats on a tank of water with oil of relative density $0.5$ to a height of $4 \mathrm{cm}$ above water. When the block attains equilibrium with four of its edges vertical

The spring balance $A$ reads $2 \mathrm{kg}$ with a block $m$ suspended from it. $A$ balance $B$ read $5 \mathrm{kg}$ when a beaker with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid in the beaker as shown in the figure. In this situation

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

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 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)

A ball floats on the surface of water in a container exposed to the atmosphere. Volume $V_1$ of its volume in inside the water. If the container is now covered and the air is pumped out. Now let $V_2$ be the volume immersed in water, then

(Density of air ${\rho }_a=1.204 \mathrm{kg} {\mathrm{m}}^{-3}$)

A piece of steel has a weight $W$ in air, $W_1$ when completely immersed in water and $W_2$ when completely immersed in an unknown liquid. The relative density (specific gravity) of liquid is

A block of density $\mathrm{\rho }$ floats in a liquid with its one third volume immersed. The density of the liquid is

A body having volume $V$ is floating, fully submerged in a liquid of density $\rho$. If the container starts moving upward with constant acceleration $\frac{g}{3}$ then the buoyant force acting on the body will become

A slender homogeneous rod of length $2\mathrm{L}$ floats partly immersed in water being supported by a string fastened to one of its end. The specific gravity of the rod is $0.75$. The length of rod that extends out of water is

A sphere of radius $R$ and made of material of relative density $1.5$ has a concentric cavity of radius $r$. It just floats when placed in a tank full of water. The value of $R/r$ will be

A wooden cube just floats inside water when a $0.2\mathrm{kg}$ mass is placed on it. When the mass is removed, the cube is $2\mathrm{cm}$ above the water level, what is the size of each side of cube?