A uniform rod of length 212 cm is bent at its midpoint into a right angle. Then

Question

A uniform rod of length 212 cm is bent at its midpoint into a right angle. Then the bent rod is placed along the positive x and positive y axes, with the "bend point" located at the origin. What is the x coordinate of the center of mass of this object? (in cm)

Now consider the situation where we change something about the rod. The changes below are each starting from the original rod (they are not a sequence of three changes). If one thing is changed at a time, leaving all of the other factors the same as described above, which of the following statements are true?

1.If the bent rod moves 20 cm to the right, then the center of mass will shift by 20 cm to the right.

2.If the mass of the rod doubles, then the location of the center of mass will move farther away from the origin.

3.If the rod doubles in length, then the location of the center of mass will move farther away from origin.

Explanation / Answer

We assumes that the bar is positioned like the letter L,and that mass of each half is mHalf

    mHalf =totalmass/2

The length of each half is =212/2

                                         =106cm

For cener of mass*coordinate

X bar =(mHalf*0+mHalf*106)/mHalf+mHalf

                                         =53cm

So X coordinate of cener of object =53cm

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