Answer to Question #223775 in Physics for Ekott Jnŕ

Question

In air an object weighs 12N, when immersed in water it weighs 15N, when immersed in another liquid, it weighs 12N, determine the density of the object and density of the other liquid

Answer 1

First things first: the weight of a body in air cannot be grater than the weight of an object in water. So, we assume that the weight in air is 15 N and weight in water is 12 N.

In air the weight is:

$$W_1=\rho gV.$$

In water:

$$W_2=W_1-F_b=W_1-\rho_wgV,\\\space\\ V=\frac{W_1-W_2}{\rho_wg}.$$

Substitute this in the equation for weight in air:

$$W_1=\rho g\frac{W_1-W_2}{\rho_wg}=\rho\frac{W_1-W_2}{\rho_w},\\\space\\ \rho=\rho_w\frac{W_1}{W_1-W_2}=5000\text{ kg/m}^3.$$

Since the weight of the object in another liquid is 12 N as well, the density of that liquid is 1000 kg/m³