An object weighs 7.84 N when it is in air and 6.86 N when it is immersed in water of density 1000 kg/m³.What is the density of the object? A)6000 kg/m³ B)7000 kg/m³ C)8000 kg/m³ D)9000 kg/m³

Question

Quizplus · Accepted Answer

The buoyant force on the object when it is immersed in water is given by:

Fb = rhoVg

where rho is the density of water, V is the volume of the object submerged in water, and g is the acceleration due to gravity.

We can find the volume of the object submerged in water by using the fact that the weight of the object reduced by the weight of the water displaced by the object gives the buoyant force:

6.86 N = 7.84 N - rhoVg

Solving for V, we get:

V = (7.84 N - 6.86 N)/(1000 kg/m^3 x 9.81 m/s^2) = 0.0100 m^3

The weight of the object is given by:

W = rho_objectVg

so we can solve for rho_object:

rho_object = W/(Vg) = 7.84 N/(0.0100 m^3 x 9.81 m/s^2) = 8000 kg/m^3

Therefore, the density of the object is 8000 kg/m^3, which corresponds to choice C.

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