The coordinates for the center of mass for the extended object shown in figure are (L/4,-L/5).What are the coordinates of the 2-kg mass?
A)(0,0)
B)(-L,
C)(-0.375 L,0.1
D)(-4 L,5
E)(-5 L,4

Question

The coordinates for the center of mass for the extended object shown in figure are (L/4,-L/5).What are the coordinates of the 2-kg mass? 
A)(0,0) 
B)(-L,
C)(-0.375 L,0.1 
D)(-4 L,5 
E)(-5 L,4

Quizplus · Accepted Answer

The coordinates of the center of mass for the extended object are (L/4,-L/5), which means that the weighted average of the coordinates of all the masses in the object is equal to (L/4,-L/5). If we let x and y be the coordinates of the 2-kg mass, then we can set up the following equation:

(1 kg)(L/2) (0,0) + (2 kg)(x,y) = (3 kg)(L/4,-L/5)

Simplifying this equation, we get:

(L/2, 0) + (2x, 2y) = (3L/4, -3L/5)

Combining like terms, we get:

(2x + L/4, 2y) = (3L/4, -3L/5)

Solving for x and y, we get:

x = -0.375 L
y = 0.1 L

Therefore, the coordinates of the 2-kg mass are (-0.375 L, 0.1 L), which corresponds to choice C.

The Coordinates for the Center of Mass for the Extended