Question

An object is solid throughout. When the object is completely submerged in ethyl alcohol, its apparent weight is 15.5 N. When completely submerged in water, its apparent weight is 12.4 N. What is the volume of the object?

Answer 1

The force opposing an object submerged in a fluid is equal in magnitude to the weight of the fluid it's displacing. Let the object have volume \(V\), mass \(m\), volume density of water \(\rho_{w}\), and volume density of ethyl \(\rho_e\). When it is submerged in ethyl, the weight and the fluid displacement force must equal the apparent weight \(W_e\).\[mg -\rho_e Vg = W_e\]Similarly, for apparent weight in water \(W_w\), we have the following.\[mg -\rho_w Vg = W_w\]Now, subtract the first equation from the second and solve for \(V\).\[\rho_e Vg - \rho_wVg = W_w - W_e\]\[\boxed{\displaystyle V=\frac{W_w - W_e}{g(\rho_e - \rho_w)}}\]We already know \(W_w\) and \(W_e\) and I know \(\rho_w=1\frac{\text{g}}{\text{cm}^3}\), so you'll just have to look up and evaluate in \(\rho_e\).