Archimedes' Principle

A $200 \mathrm{g}$ solid block of Aluminium (Density of Al = $2.70 \mathrm{g}/\mathrm{cc}$) is placed in a beaker of water filled to the brim. Some water overflows. The same is done in another beaker with a $200 \mathrm{g}$ solid block of lead (Density of lead = $11.3 \mathrm{g}/\mathrm{cc}$). Does the block of lead displace more, less, or the same amount of water as the aluminium block?

A $200$ g solid block of Aluminium (Density of Al = $2.70$ g/cc) is placed in a beaker of water filled to the brim. Some water overflows. The same is done in another beaker with a $800$ g solid block of lead (Density of lead = $11.3$ g/cc). Does the block of lead displace more, less, or the same amount of water as the aluminium block?

Two cylinders of same cross-section area and length $L$ but made of two material of densities $d_1$ and $d_2$ are cemented together to form a cylinder of length $2L$. The combination floats in a liquid of density $d$ with a length$\frac{L}{2}$above the surface of the liquid. If $d_1>d_2$, then

A cork of density $0.5 \mathrm{g} {\mathrm{cm}}^{-3}$ floats on a calm swimming pool. The fraction of the cork's volume which is under water is

A container of large surface area is filled with liquid of density $\text{ρ}$ . A cubical block of side edge a and mass M is floating in it with four-fifth of its volume submerged. If a coin of mass m is placed gently on the top surface of the block is just submerged. M is

Two bodies having volumes $V$ and $2V$ are suspended from the two arms of a common balance and they are found to balance each other. If larger body is immersed in oil (density $d_1=0.9 \mathrm{g} {\mathrm{cm}}^{-3}$) and the smaller body is immersed in an unknown liquid, then the balance remain in equilibrium. The density of unknown liquid is given by

A slender homogeneous rod of length 2L floats partly immersed in water, being supported by a string fastened to one of its ends, as shown. The specific gravity of the rod is 0.75. The length of rod that extends out of water is

A cuboidal piece of wood has dimensions a, b and c. Its relative density is d. It is floating in a large body of water such that side a is vertical. It is pushed down a bit and released. The time period of SHM executed by it is

Two cubes of size $1.0 \mathrm{m}$ sides, one of relative density $0.60$ and another of relative density $=1.15$ are connected by weightless wire and placed in a large tank of water. Under equilibrium the lighter cube will project above the water surface to a height of

Some liquid is filled in a cylindrical vessel of radius $R$. Let $F_1$_​ be the force applied by the liquid on the bottom of the cylinder. Now the same liquid is poured into a vessel of uniform square cross-section of side $R$. Let $F_2$ be the force applied by the liquid on the bottom of this new vessel. Then

An expansible ballon filled with air floats on the surface of a lake with 2/3 of its volume submerged. How deep must it be sunk in the water so that it is just in equilibrium neither sinking further nor rising ? It is assumed that the temperature of the water is constant & that the height of the water barometer is 9 meters

In air an object weighs 15N, when immersed completely in water the same object weighs 12N. When immersed in another liquid completely, it weighs 13N. Find the specific gravity of the object.

A sphere of volume $\mathrm{V}$ is made of a material with lower density than water. While on Earth, it floats on water with its volume $f_{1}V\left(f_1<1\right)$ sub merged. On the other hand, on a spaceship accelerating with acceleration $a<g$ ($g$ is the acceleration due to gravity on Earth) in outer space, its submerged volume in water is $f_{2}V$. Then:

A stone of density $2000 \mathrm{kg} {\mathrm{m}}^{-3}$ completely immersed in a lake is allowed to sink from rest. If the effect of friction is neglected, then after$4$seconds, the stone will reach a depth of

A small ball of mass $M$ and density $\rho$ is dropped in a viscous liquid of density ${\rho }_0$. After some time, the ball falls with a constant velocity. What is the viscous force on the ball?

A spherical ball of unknown material of radius$R$ has a concentric cavity of radius $\frac{R}{3}$ inside it. The sphere is found to just float in water with the highest point of it touching the water surface. Density of the material of the sphere (in $\mathrm{g} {\mathrm{cc}}^{-1}$)

A piece of wax weighs $x \mathrm{g}$ in air. A piece of metal is found to weigh $y \mathrm{g}$ in water. It is tied to the wax and both together weigh $z \mathrm{g}$ in water. Then, the specific gravity of wax is: ($z>y$)

A stone of density$2000 \mathrm{kg} {\mathrm{m}}^{-3}$ completely immersed in a lake is allowed to sink from rest. If the effect of friction is neglected, then after $4$seconds, the stone will reach a depth of

A metal ball of density $7800 \mathrm{kg} {\mathrm{m}}^{-3}$ is suspected to have a large number of inner cavities. It weighs $9.8 \mathrm{kg}$ when weighed directly on a balance and $1.5 \mathrm{kg}$ less when immersed in water. The fraction by volume of the cavities in the metal ball is approximately:
 

An ice-cube of edge is $10 \mathrm{cm}$10 cm floating in water. Time period of small vertical oscillations of the cube is
(Specific gravity of ice is $0.9$)