/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 106 A sphere of radius 1 in., made f... [FREE SOLUTION] | 91影视

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Chapter 3: Problem 106

A sphere of radius 1 in., made from material of specific gravity of \(\mathrm{SG}=0.95,\) is submerged in a tank of water. The sphere is placed over a hole of radius 0.075 in., in the tank bottom. When the sphere is released, will it stay on the bottom of the tank or float to the surface?

Short Answer

Expert verified
Since \(W < F_b\), the sphere will float to the surface and not stay at the bottom of the tank.

Step by step solution

01

Calculate the weight of the sphere

We know that the volume \(V\) of a sphere is given by the formula \(V = \frac{4}{3} \pi r^3\), where \(r\) is the radius. Using \(r=1\) in, we get \(V = \frac{4}{3} \pi\). As weight of the sphere \(W = V \times g \times SG\), where \(g\) is the acceleration due to gravity, we have \(W = \frac{4}{3} \pi \times g \times 0.95\).
02

Calculate the buoyant force acting on the sphere

The buoyant force \(F_b\) acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. Since the sphere is fully submerged, the fluid displaced is equal to the volume of the sphere, which is equal to the weight of the water displaced. Therefore, \(F_b = V \times g = \frac{4}{3} \pi \times g\). The volume of the sphere in the buoyant force formula is the same as the volume in the weight formula because the sphere is fully submerged.
03

Compare the weight of the sphere with the buoyant force

If \(W > F_b\), the sphere will sink. If \(W = F_b\), the sphere will float. If \(W < F_b\), the sphere will rise. Since \(W =\frac{4}{3} \pi \times g \times 0.95\) and \(F_b =\frac{4}{3} \pi \times g\), comparing \(W\) and \(F_b\) yields \(W < F_b\) because \(0.95 < 1\).

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Most popular questions from this chapter

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