JEE Mains · Physics · STD 11 - 6. system of particles and rotational motion
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
- A \(\frac{{3h}}{4}\)
- B \(\;\frac{{5h}}{8}\)
- C \(\;\frac{{3{h^2}}}{{8R}}\)
- D \(\;\frac{{{h^2}}}{{4R}}\)
Answer & Solution
Correct Answer
(A) \(\frac{{3h}}{4}\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{l} {y_{cm}} = \frac{{\int {ydm} }}{{\int {dm} }}\\ \,\,\,\,\,\,\,\, = \frac{{\int\limits_0^h {\pi {r^2}dy\rho \times y} }}{{\frac{1}{3}\pi {R^2}h\rho }} = \frac{{3h}}{4} \end{array}\)
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