Question 209: Centre of Mass and Rotational Motion

Question

Distance of the center 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 :

Accepted Answer

Let the density of solid cone $$ho $$.
$$dm = ho \pi {r^2}dy$$
$${y_{cm}} = {{\int {ydm} } \over {\int {dm} }}$$
$$ = {{\int\limits_0^h {\pi {r^2}} dyho  	imes y} \over {{1 \over 3}\pi {R^2}hho }}$$
$$ = {{3h} \over 4}$$

Answer

$${{5h} \over 8}$$

Answer

$${{3{h^2}} \over {8R}}$$

Answer

$${{{h^2}} \over {4R}}$$

Answer

$${{3h} \over 4}$$

Centre of Mass and Rotational Motion

Distance of the center 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 :

Choose the correct answer: