Distance of the centre of mass of a solid uniform cone from its v… - Vidyadip

MCQ

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

✓
$\frac{{3h}}{4}$
B
$\;\frac{{5h}}{8}$
C
$\;\frac{{3{h^2}}}{{8R}}$
D
$\;\frac{{{h^2}}}{{4R}}$

✓

Answer

Correct option: A.

$\frac{{3h}}{4}$

a
$\begin{array}{l}
{y_{cm}} = \frac{{\int {ydm} }}{{\int {dm} }}\\
\,\,\,\,\,\,\,\, = \frac{{\int\limits_0^h {\pi {r^2}dy\rho \times y} }}{{\frac{1}{3}\pi {R^2}h\rho }} = \frac{{3h}}{4}
\end{array}$

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