Archimedes Principle and Buoyancy

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.

If there were no gravity, which of the following will be not there for a fluid?

If $w_1=$ weight of a body and $w_2=$ buoyant force exerted by the liquid on it, then the body will remain floating with some portion of it above the liquid surface when -

A very large block of ice of the size of a volleyball court and of uniform thickness of $8 m$ is floating on water. A person standing near its edge wishes to fetch a bucketful of water using a rope. The smallest length of rope required for this is about

A block of wood is floating on water at $0°C$ with volume $V_0$ above water. When the temperature of water increases from $0$ to $10°C,$ the change in the volume of the block that is above water is best described schematically by the graph.

A body is suspended by a light string. The tensions in the string when the body is in air, when the body is totally immersed in water and when the body is totally immersed in a liquid are respectively $40.2 \mathrm{N},28.4 \mathrm{N}$ and $16.6 \mathrm{N}$. The density of the liquid is

A coin is embedded in a ice cube floating in water in a graduated cylinder. If the ice cube melts, then the level of water

A ball of mass $10 \mathrm{kg}$ and density $1 \mathrm{g} {\mathrm{cm}}^{-3}$ is attached to the base of a container having a liquid of density $1.1 \mathrm{g} {\mathrm{cm}}^{-3}$, with the help of a spring as shown in the figure. The container is going up with an acceleration $2 \mathrm{m} {\mathrm{s}}^{-2}$. If the spring constant of the spring is $200 \mathrm{N} {\mathrm{m}}^{-1}$, the elongation in the spring is

A man is sitting in a boat that is floating in a pond. Now the man drinks some water from the pond, what happens to the level of water in the pond?