A solid rock,suspended in air by a spring scale,has a measured mass of 8.50 kg.When the rock is submerged in water,the scale reads 3.50 kg.What is the density of the rock? (water density = 1 000 kg/m³) A) 0.71 × 10³ kg/m³ B) 0.7 × 10³ kg/m³ C) 0.29 × 10³ kg/m³ D) 1.7 × 10³ kg/m³ E) 2.2 × 10³ kg/m³

Question

Quizplus · Accepted Answer

The buoyant force on the submerged rock is equal to the weight of the water displaced by the rock. This buoyant force reduces the apparent weight of the rock measured by the scale from its actual weight.

The weight of the water displaced by the rock is:

w = mg - F_B = 8.50 kg x 9.81 m/s^2 - 3.50 kg x 9.81 m/s^2 = 48.97 N

where g is the acceleration due to gravity and F_B is the buoyant force.

The volume of water displaced by the rock is equal to the volume of the rock. The density of the water is 1000 kg/m^3. Therefore, the volume of the rock is:

V = m_water / rho_water = w / rho_water x g = 48.97 N / (1000 kg/m^3 x 9.81 m/s^2) = 0.00499 m^3

The density of the rock is:

rho_rock = m_rock / V = 8.50 kg / 0.00499 m^3 = 1703.41 kg/m^3

Rounding to two significant digits, we get 1.7 × 10^3 kg/m^3 or 1.7 × 10^15 g/cm^3. The correct option is D.

A Solid Rock,suspended in Air by a Spring Scale,has a Measured