Distance of the centre of mass of a solid uniform cone from its vertex is $\mathrm{z}_{0}$. If the radius of its base is R and its height is h then $\mathrm{z}_{0}$ is equal to :

JEE Main · 2015 · 04 Apr 2015 · Offline · Conservation of Momentum

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

Answer: (A)

Solution

A uniform solid cone carries more of its material near the wide base, so its centre of mass sits one-quarter of the height up from the base, at

h /4

. Measured instead from the pointed vertex at the top, that is

z_{0} = h - \frac{h}{4} = \frac{3 h}{4}

. Notice the base radius never enters -- only the height fixes this axial position.

JEE Main · 2015 · 04 Apr 2015 · Offline · Single correct option

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