00:01
In this question we are required to calculate where will this center of mass of this solid cone will lie.
00:07
Alright, so if this is the cone, all right, let us say at some distance h, if this is some distance h, this would be, let us say radius of this complete cone was r and this height was capitalized.
00:34
So if this is small r and this is h, then we can relate it, r, r over h is equal to small r over h.
00:42
So small r will be equal to r by h into h.
00:48
This will be radius at any height h.
00:50
So over here at any height at any height as we will take a disk of radius r and thickness d .h like this.
01:03
So to calculate the mass, what we will do, calculate the location of center of mass.
01:09
This disc will have a radius r so the area of this is pi r square into d h is the thickness so this would be the volume into density this will be the mass and location of this mass from this from this origin is h distance away all right as we know that x bar is equal to sigma x i m i over sigma m i this is how we calculate the location of center of mass so divide it by this is our my this is our x i and summation of my will be mass of this whole so row into one by three pi r square into h this is capital r so this is the complete mass so this would be h bar h bar means the height above which the center of mass will lie.
02:15
So pi cancels out.
02:19
So this will become r square h d h over this three will come up.
02:30
So r squared into h...