If two liquids of density `rho_1` and `rho_2` are mixed with each other maintaing equal to volume then show that the density of the mixture will be `1/2 (rho_1+ rho_2)`

(i) Prove that the density of the mixture of two substances with densities rho_(1)andrho_(2) of equal mass will be (2rho_(1)rho_(2))/(rho_(1)+rho_(2)) . (ii) Prove that if the two substance with densities rho_(1)andrho_(2) are mixed in equal volumes, then the density of the mixture thus formed will be 1/2(rho_(1)+rho_(2))

If two bodies of density rho_1 and rho_2 are mixed at same mass, then the density of the mixture will be p = (2rho_1rho_2)/(rho_1+rho_2) . [show that].

A hollow right circular cone of height h and of semivertical angle theta is placed with its base on a horizontal table. If the cone is filled with a liquid of density rho and the weight of the empty cone is equal to the weight of the liquid that it contains, find the thrust of the liquid on the base of the cone and the pressure exerted on the table.

A liquid of mass m_(1) and density rho_(1) is mixed with another liquid of mass m_(2) and density rho_(2) . If the volume of the mixture does not change, then what will be the density of the mixture?

To determine the composition of a bimetallic alloy, a sample is first weighed in air and then in water. These weights are found to be w_1 and w_2 respectively. If the densities of the two constituent metals are rho_1 and rho_2 respectively, then the weight of the first metal in the sample is (where rho_w is the density of water)

A solid spherical ball and a hollow spherical ball of two different materials of densities rho_(1) and rho_(2) respectively have same outer radii and same mass. What will be the ratio of the moment of inertia ( about an axis passing through the centre ) of the hollow sphere to that of the solid sphere?

If a body weighs m_1 gm-wt in air of density d and m_2 g-wt in a liquid of density D show that the density of the material of the body = ((m_1D)/(m_1-m_2)-(m_2d)/(m_1-m_2))gm//cm^2 .

A cylindrical block floats vertically in a liquid of density rho_(1) kept in a container such that the fraction of volume of the cylinder inside the liquid is x_(1) . Then some amount of another immiscible liquid of density rho_(2) (rho_(2) lt rho_(1)) is added to the liquid in the container so that the cylinder now floats just fully immersed in the liquids with x_(2) fraction of volume of the cylinder inside the liquid of density rho_(1) . The ratio rho_(1)//rho_(2) will be