JEE Mains · Physics · STD 11 - System of particles and rotational motion
- JEE Mains 2015
- Hard
- 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
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \(\frac{{3h}}{4}\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{l}
{y_{cm}} = \frac{{\int {ydm} }}{{\int {dm} }}\\
\,\,\,\,\,\,\,\, = \frac{{\int\limits_0^h {\pi {r^2}dy\rho \times y} }}{{\frac{1}{3}\pi {R^2}h\rho }} = \frac{{3h}}{4}
\end{array}\)
{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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