How to get horizontal distance between point of contact and point P ?
2026-03-25 11:04:48.1774436688
How to take moment about point of contact in a hemisphere?
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Let $A$ be the center of the hemisphere (on the circular face), $B$ the center of mass of the hemisphere, $C$ the point of contact.
Extend a horizontal line from $C$. Drop a vertical line from $A$ to meet the horizontal line at $D$. This same vertical line also goes through $B$.
So now the horizontal distance of either $A$ or $B$ to $C$ is known to equal the distance $CD.$
Consider triangle $\triangle ADC.$ It is a right triangle with hypotenuse $a$ and the angle at vertex $A$ (opposite the side $CD$) is $\alpha$. (Look at the relationships of perpendicular lines in the figure to see why.) Now you can use the sine formula to find the length of $CD.$