Question Number 105073 by Dwaipayan Shikari last updated on 25/Jul/20

 Find the centre of the mass of a cone of height ′H′ and Radius  ′R′

Commented byajfour last updated on 25/Jul/20

solid cone or hollow ?

Commented byDwaipayan Shikari last updated on 25/Jul/20

Solid sir

Commented bymr W last updated on 25/Jul/20

Commented bymr W last updated on 25/Jul/20

for a solid cone the distribution of  mass is a parabola of second order,  therefore y_S =(H/4).

Answered by ajfour last updated on 25/Jul/20

Commented byajfour last updated on 25/Jul/20

y_(cone) = ((∫_0 ^(  h) ρ(h−y)πr^2 dy)/(ρ((1/3))πR^2 h))    (r/y)=(R/h)   ⇒  r^2 =((R/h))^2 y^2   y_(cone) = ((∫_0 ^(  h) ρ(h−y)π((R/h))^2 y^2 dy)/(ρ((1/3))πR^2 h))        = (3/h^3 )∫_0 ^(  h) (hy^2 −y^3 )dy        = (3/h^3 )(((hy^3 )/3)−(y^4 /4))∣_0 ^h       y_(cone)  = (3/h^3 )((h^4 /3)−(h^4 /4)) = (h/4) .

Commented byDwaipayan Shikari last updated on 25/Jul/20

Kindly can you tell me how to draw such diagrams?⊛

Commented byajfour last updated on 25/Jul/20

i use lekh diagram app.

Commented byDwaipayan Shikari last updated on 25/Jul/20

😃👍💪