Q. 19 A sphere completely submerged in... [FREE SOLUTION]

Chapter 14: Q. 19 (page 384)

A sphere completely submerged in water is tethered to the bottom with a string. The tension in the string is one-third the weight of the sphere. What is the density of the sphere?

Short Answer

Expert verified

The density of the sphere if tension within the string is one-third the load of the sphere, $蚁_{b} = 750 kg / m 3$

Step by step solution

Newton's first law.

The law of inertia, often referred to as Newton's first law, states that if a body is at rest or occupation a line at a relentless speed, it will remain at rest or still move in an exceedingly straight path at a continuing speed until it's acted with by a force.

Derive the Force.

Using the information provided within the exercise and Newton's first law, with the positive direction upwards, we will write:

$F_{B} - T - F_{g} = 0 鈬� F_{B} = F_{G} + T = \frac{4}{3} m g$

Find the density.

Knowing the buoyant force formula and expressing the ball's mass as $m = 蚁_{b} V$ , we may write:

$蚁_{w} g V = \frac{4}{3} 蚁_{b} V g 鈬� 蚁_{b} = \frac{3}{4} 蚁_{w}$

Because we all know the density of water, we will calculate the numerical solution as,

$蚁_{b} = \frac{3}{4} 脳 1000 = 750 kg / m 3$

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91影视

A sphere completely submerged in water is tethered to the bottom with a string. The tension in the string is one-third the weight of the sphere. What is the density of the sphere?

Short Answer

Step by step solution

Newton's first law.

Derive the Force.

Find the density.

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