An object weighs 60.0N in air, 48.2N in a certain liquid X, and 44.9N in water, Calculate the relative density of X

Weight of object in air (W_air): 60.0 N

Weight of object in liquid X (W_X): 48.2 N

Weight of object in water (W_water): 44.9 N

The loss of weight in a fluid is equal to the buoyant force, which is equal to the weight of the displaced fluid.

Buoyant force in water: 𝐹buoyant, water=𝑊air−𝑊water=60.0 N−44.9 N=15.1 NFbuoyant, water​=Wair​−Wwater​=60.0N−44.9N=15.1N

Since the buoyant force is equal to the weight of the water displaced and the density of water (ρ_water) is 1 g/cm³ (or 1000 kg/m³), the volume of the object (V) can be calculated using:

𝐹buoyant, water=𝜌water⋅𝑉⋅𝑔Fbuoyant, water​=ρwater​⋅V⋅g 15.1 N=1000 kg/m3⋅𝑉⋅9.8 m/s215.1N=1000kg/m3⋅V⋅9.8m/s2 𝑉=15.1 N1000 kg/m3⋅9.8 m/s2V=1000kg/m3⋅9.8m/s215.1N​ 𝑉≈1.54×10−3 m3V≈1.54×10−3m3

Buoyant force in liquid X:

𝐹buoyant, X=𝑊air−𝑊X=60.0 N−48.2 N=11.8 NFbuoyant, X​=Wair​−WX​=60.0N−48.2N=11.8N

Using the same volume V (since the object's volume doesn't change), the density of liquid X (ρ_X) can be calculated:

𝐹buoyant, X=𝜌X⋅𝑉⋅𝑔Fbuoyant, X​=ρX​⋅V⋅g 11.8 N=𝜌X⋅1.54×10−3 m3⋅9.8 m/s211.8N=ρX​⋅1.54×10−3m3⋅9.8m/s2 𝜌X=11.8 N1.54×10−3 m3⋅9.8 m/s2ρX​=1.54×10−3m3⋅9.8m/s211.8N​ 𝜌X≈786.1 kg/m3ρX​≈786.1kg/m3

Relative density of liquid X: The relative density (specific gravity) is the ratio of the density of liquid X to the density of water: Relative density=𝜌X𝜌water=786.1 kg/m31000 kg/m3≈0.786Relative density=ρwater​ρX​​=1000kg/m3786.1kg/m3​≈0.786

Therefore, the relative density of liquid X is approximately 0.786.