Center of Mass In Exercises 59 and 60, find the mass and the indicated coordinate of the center of mass of the solid region Q of density bounded by the graphs of the equations.
Find using .
To calculate: The mass and the indicated coordinate of center of mass of solid region with density given as . The solid region is bounded by the graph of equation .
The density of solid region is and the solid is bounded by the graph of equation,
Mass of a solid region having density is,
First moment about plane is,
Coordinate of center of mass of a solid region is,
A 3-D plot is made with the help of maple software,
The limits of and can be calculated with the help of this 3-D plot.
Take the provided equation of the solid into consideration.
In the above equation, the bounds of is and bounds of is,
Take the plane into consideration.
In this case, since the value of , the equation of the line will be given as,
The lower limit of is provided in the question, i.e.,
On applying the formula for the mass of solid body , we get,
On integrating with respect to , we get,
Further, on integrating with respect to , we get,
Thus, mass of the solid body is,
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