The center of mass of a lamina in the shape of a region in the xy-plane bounded by the x-axis, x = 3, y = 2 and the y-axis with area density $\rho ( x , y ) = x y ^ { 2 }$ is

A) $\left( - 1 , \frac { 3 } { 4 } \right)$
B) $\left( 1 , - \frac { 3 } { 4 } \right)$
C) $\left( 1 , \frac { 3 } { 4 } \right)$
D) $\left( - 1 , - \frac { 3 } { 4 } \right)$
E) $\left( 1 , \frac { 3 } { 2 } \right)$

Question

The center of mass of a lamina in the shape of a region in the xy-plane bounded by the x-axis, x = 3, y = 2 and the y-axis with area density $\rho ( x , y ) = x y ^ { 2 }$ is

A) $\left( - 1 , \frac { 3 } { 4 } \right)$
B) $\left( 1 , - \frac { 3 } { 4 } \right)$
C) $\left( 1 , \frac { 3 } { 4 } \right)$
D) $\left( - 1 , - \frac { 3 } { 4 } \right)$
E) $\left( 1 , \frac { 3 } { 2 } \right)$

Quizplus · Accepted Answer

The center of mass is calculated using the formulas for $ \bar{x} $ and $ \bar{y} $ which involve integrating the density function over the given region. For this problem, the correct center of mass is $\left( 1 , \frac { 3 } { 2 } \right)$.

The Center of Mass of a Lamina in the Shape ρ(x,y)=xy2\rho ( x , y ) = x y ^ { 2 }ρ(x,y)=xy2

The Center of Mass of a Lamina in the Shape $\rho ( x , y ) = x y ^ { 2 }$