A wooden ball is tied to the bottom of a swimming pool by a string. What is the tension in the string if the ball's diameter is 0.15 m and its mass is 144 g? The water in the pool is fresh water, density 1,000 kg/m³. A) 15.9 N B) 12.7 N C) 14.1 N D) 1.78 N

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Quizplus · Accepted Answer

The tension in the string is equal to the weight of the ball minus the buoyant force acting on the ball. The weight of the ball is given by:$$W = mg$$where:* W is the weight of the ball in newtons* m is the mass of the ball in kilograms* g is the acceleration due to gravity in meters per second squaredThe buoyant force acting on the ball is given by:$$F_b = \rho Vg$$where:* Fb is the buoyant force in newtons* ρ is the density of the fluid in kilograms per cubic meter* V is the volume of the ball in cubic meters* g is the acceleration due to gravity in meters per second squaredThe volume of the ball is given by:$$V = \frac{4}{3}\pi r^3$$where:* V is the volume of the ball in cubic meters* r is the radius of the ball in metersSubstituting the given values into the equations above, we get:$$W = (0.144 kg)(9.81 m/s^2) = 1.41 N$$$$F_b = (1000 kg/m^3)(\frac{4}{3}\pi (0.075 m)^3)(9.81 m/s^2) = 1.27 N$$$$T = W - F_b = 1.41 N - 1.27 N = 0.14 N$$Therefore, the tension in the string is 0.14 N.

A Wooden Ball Is Tied to the Bottom of a Swimming