Question

Three balls with the same radius 21 cm are in water. Ball 1 floats, with

half of it exposed above the water level. Ball 2, with a density 893
kg/m3 is held below the surface by a cord anchored to the bottom of the
container, so that it is fully submerged. Ball 3, of density 1320 kg/m3, is
suspended from a rope so that it is fully submerged. Assume the
density of water is 1000 kg/m3 in this problem.
A. Which is true for Ball 1?
B. What is the tension on the rope holding the second ball, in newtons?
C. What is the tension on the rope holding the third ball in N?

Answer 1

Ball 1 floats with half exposed above water level. Tension on rope holding Ball 2 is calculated using weight and buoyant force. Tension on rope holding Ball 3 is equal to buoyant force.

Step-by-step explanation:

A. Ball 1 is floating with half of it exposed above the water level.

This means that the buoyant force on the ball is equal to the weight of the ball.

Since the buoyant force is greater than the weight of the ball, the ball floats.

B. The tension on the rope holding Ball 2 can be found using the equation:

Tension = Weight - Buoyant force.

The weight of the ball is calculated by multiplying its volume by its density and acceleration due to gravity.

The buoyant force can be found by multiplying the volume of the ball submerged in water by the density of water and acceleration due to gravity.

C. The tension on the rope holding Ball 3 is the same as the buoyant force acting on it.

The buoyant force can be found by multiplying the volume of the ball submerged in water by the density of water and acceleration due to gravity.

Answer 2

Step-by-step explanation:

A )

The ball floats with half of it exposed above the water level . So it must have density half that of water . In other words its density must have been 500 kg / m³

B )

Tension in the ball will be equal to net force acting on the ball

Net force on the ball = buoyant force - weight .

4/3 x π x .21³ x 10⁻⁶ x 9.8 ( 1000 - 893 )

= 40.65 x 10⁻⁶ N .

C )Tension in the 3 rd ball will be equal to net force acting on the ball

Net force on the ball = weight - buoyant force

= 4/3 x π x .21³ x 10⁻⁶ x 9.8 ( 1320 - 1000 )

= 121.6 x 10⁻⁶ N .