A plastic ball fully submerged in water is tied to the bottom of the container using a string as shown. If the volume of the plastic ball is 57 cm3 and its density is 661 kg/m3, find the tension, in Newton, in the string? Density of water is 1000 kg/m3.

To find the tension in the string, we first need to find the buoyant force acting on the ball. The buoyant force can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object.

Step 1: Convert the volume of the ball from cm^3 to m^3. 1 m^3 = 1,000,000 cm^3 So, 57 cm^3 = 57 / 1,000,000 = 0.000057 m^3

Step 2: Calculate the weight of the water displaced by the ball. The weight of the water displaced is equal to the volume of the ball times the density of water times the acceleration due to gravity. Weight of water displaced = Volume of ball * Density of water * g = 0.000057 m^3 * 1000 kg/m^3 * 9.8 m/s^2 = 0.5586 N

Step 3: Calculate the weight of the ball. The weight of the ball is equal to the volume of the ball times the density of the ball times the acceleration due to gravity. Weight of ball = Volume of ball * Density of ball * g = 0.000057 m^3 * 661 kg/m^3 * 9.8 m/s^2 = 0.3533586 N

Step 4: Calculate the tension in the string. The tension in the string is equal to the weight of the ball minus the buoyant force (which is the weight of the water displaced). Tension = Weight of ball - Weight of water displaced = 0.3533586 N - 0.5586 N = -0.2052414 N

Since tension cannot be negative, we take the absolute value, which gives us the tension in the string as 0.2052414 N.