An object weighs 15 N in air and 13 N when submerged in mineral spirits, which has a density of 788 kg/m³. Determine the density of the object. A)330 kg/m³ B)500 kg/m³ C)1.2 × 10³ kg/m³ D)5.9 × 10³ kg/m³ E)7.5 × 10³ kg/m³

Question

Quizplus · Accepted Answer

The buoyant force (B) acting on the object equals the weight of the displaced liquid, given by:

B = ρfluid * V * g

where ρfluid is the density of the liquid, V is the volume of the displaced liquid (equal to the volume of the submerged object), and g is the acceleration due to gravity.

The weight (W) of the object in air is given as 15 N, so its mass can be found as:

W = m * g -> m = W/g = 15 N / 9.81 m/s^2 ≈ 1.53 kg

The weight of the object in the liquid is 13 N, so the buoyant force acting on it is:

B = W - 13 N = 2 N

Substituting the values, we get:

2 N = 788 kg/m^3 * V * 9.81 m/s^2

Solving for V, we get:

V = 2 N / (788 kg/m^3 * 9.81 m/s^2) ≈ 0.000255 m^3

The volume of the object is the same as the volume of the displaced liquid, so its density can be found as:

ρobject = m / V = 1.53 kg / 0.000255 m^3 ≈ 6000 kg/m^3

Rounding to two significant figures, the answer is D) 5.9 × 10^3 kg/m^3.

An Object Weighs 15 N in Air and 13 N