$A$ body of density $d_1$ is counterpoised by $M$ of weights of density $d_2$ in air of density $d$. Then the true mass of the body is

$A$ piece of metal weighs $45 \ g$ in air and $25 \ g$ in a liquid of density $1.5 \times 10^3 \ kg \ m^{-3}$ kept at $30^{\circ} C$. When the temperature of the liquid is raised to $40^{\circ} C$,the metal piece weighs $27 \ g$. The density of the liquid at $40^{\circ} C$ is $1.25 \times 10^3 \ kg \ m^{-3}$. The coefficient of linear expansion of the metal is:

$A$ heavy hollow cone of radius $R$ and height $h$ is placed on a horizontal table surface,with its flat base on the table. The whole volume inside the cone is filled with water of density $\rho$. The circular rim of the cone's base has a watertight seal with the table's surface and the top apex of the cone has a small hole. Neglecting atmospheric pressure,find the total upward force exerted by water on the cone.

$A$ man is carrying a block of a certain substance (of density $1000 \,kg/m^3$) weighing $1 \,kg$ in his left hand and a bucket filled with water and weighing $10 \,kg$ in his right hand. He drops the block into the bucket. How much load does he carry in his right hand now (in $,kg$)?

An empty glass jar is submerged in a tank of water with the open mouth of the jar downwards, so that the air inside the jar is trapped and cannot escape. As the jar is pushed down slowly, the magnitude of the net buoyant force on the system of the volume of gas trapped in the jar and the jar:

$A$ solid cube and a solid sphere,both made of the same material,are completely submerged in water but at different depths. The sphere and the cube have the same surface area. The buoyant force is