Rotational Motion Question 112
Question: 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
Options:
A) $\frac{h^{2}}{4R}$
B) $\frac{3{{h}^{{}}}}{4}$
C) $\frac{5{{h}^{{}}}}{8}$
D) $\frac{3h^{2}}{8R}$
Show Answer
Answer:
Correct Answer: B
Solution:
[b]
$dm=\pi r^{2}.dy.r$
$y _{CM}=\frac{\int{ydm}}{\int{dm}}=\frac{\int _{0}^{h}{\pi r^{2}dy\times \rho \times y}}{\frac{1}{3}\pi R^{2}h\rho }=\frac{3h}{4}$
