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## Question:

A child playing in a swimming pool realizes that it is easy to push a small inflated ball under the surface of the water whereas a large ball requires a lot of force. The child happens to have a styrofoam ball (the shape of the ball will not distort when it is forced under the surface), which he forces under the surface of the water. If the child needs to supply 608 N to totally submerge the ball, calculate the diameter ???? of the ball. The density of water is ????w=1.000×103 kg/m3, the density of styrofoam is ????foam=95.0 kg/m3, and the acceleration due to gravity is ????=9.81 m/s2.

## Answer:

The **diameter** of ball **submerged** into water is of **0.5 m**.

**Given data:**

The magnitude of **force** applied by child is, ** F = 608 N**.

The **density** of water is, .

The density of **styrofoam** is, .

**Gravitational acceleration** is, .

As per the concept of **buoyancy**, the **buoyant force** (B) applied by the water is in equilibrium with the** weight of ball** (W) and **force applied** by the child (F). Therefore,

**Buoyant Force = Weight + Force applied**

The volume of ball is,

Here, **r **is the** radius** of ball.

Then** diameter of ball** is,

Thus, the diameter of the ball is **0.5 m**.

Learn more about the buoyant force here:

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