QJEEM15Phf66d: JEE Main 2015 Physics - Class 11 JEEM15Phf66d Solution: Distance of the center of mass of a solid uniform cone from its …

Question

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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

\rho

.

dm = \rho \pi {r^2}dy

{y_{cm}} = {{\int {ydm} } \over {\int {dm} }}

= {{\int\limits_0^h {\pi {r^2}} dy\rho \times y} \over {{1 \over 3}\pi {R^2}h\rho }}

= {{3h} \over 4}

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