If the wt. of a body in vacuum is W and `W_1` and `W_2` are weights when it is immersed in a liquid of specific gravity `rho_1` and `rho_2` respectively, then prove that `W=(W_1rho_2-W_2rho_1)/(rho_2-rho_1)`

The weights of a body in air and water are W and W' respectively. Prove that the apparent weight of the body when immersed in a liquid of density delta will be W''=W-(W-W')delta .

When a body of density rho and volume V is floating in a liquid of density sigma

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)

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].

The density of a body is d and that of air is rho . If the body weighs w in air, what will be its actual weight?

When a body is immersed separately into three liquids of specific gravities S_(1),S_(2)andS_(3) , its apparent weights become W_(1),W_(2)andW_(3) respectivley. Show that S_(1)(W_(2)-W_(3))+S_(2)(W_(3)-W_(1))+S_(3)(W_(1)-W_(2))=0 .

The density of a body is d and that of air is rho . Prove that the real weight of the body, weighed W in air, is W_(0)=W/(1-rho//d) .