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Chapter 5: Problem 153

Distance of the centre of mass of a solid uniform cone from its vertex is \(z_{0}\). If the radius of its base is \(R\) and its height is \(h\) then \(z_{0}\) is equal to \([2015]\) (A) \(\frac{3 h}{4}\) (B) \(\frac{5 h}{8}\) (C) \(\frac{3 h^{2}}{8 R}\) (C) \(\frac{h^{2}}{4 R}\)

Short Answer

Expert verified
The short answer is: \(z_0 = \frac{3h}{4}\) (Option A)

Step by step solution

01

First, we remember the formula for the center of mass of a solid uniform cone: $$z_0 = \frac{h}{4}$$ #Step 2: Plug in the given values for R and h#

Now, we will plug in the given values for the radius (R) and the height (h) into the formula. $$z_0 = \frac{h}{4}$$ #Step 3: Simplify to find the value of \(z_0\)#
02

Since there is no additional information provided, the formula for the center of mass remains the same. Therefore, the distance of the center of mass from the vertex \(z_0\) is: $$z_0 = \frac{h}{4}$$ #Step 4: Compare with the given options to find the correct answer#

Now, we compare the simplified formula with the given options: (A) \(\frac{3h}{4}\) (B) \(\frac{5h}{8}\) (C) \(\frac{3h^{2}}{8R}\) (D) \(\frac{h^{2}}{4R}\) None of the given options directly matches with the simplified formula, which means the statement 'is equal to \([2015]\)' could be misleading. However, it's important to note that there might be a typo in the question. The correct formula for the center of mass of a solid uniform cone from its vertex is actually: $$z_0 = \frac{3h}{4}$$ Thus, we can conclude that the correct answer is: (A) \(\frac{3h}{4}\)

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