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An object is made by hanging a ball of mass M from one end of a plank having the same mass and length L. The object is then pivoted at a point a distance L/4 from the end of the plank supporting the ball, as shown below.
Is the object balanced?
Yes
No, it will fall to the left.
No, it will fall to the right

Respuesta :

akindelemf

Answer:

Yes, the object is balanced

Explanation:

Torque  on left side ([tex]T_{L}[/tex]) = Force × Distance

                                         = Mg[tex]\frac{L}{4}[/tex]              

                                                        where, [tex]\frac{L}{4}[/tex] is the distance of mass from pivot

Torque  on left side ([tex]T_{R}[/tex]) = Force × Distance

                                         = Mg[tex]\frac{L}{4}[/tex]

Both Torque are equal but are in opposite direction.  

xero099

The object is balanced as the center of mass of the system is located at O.

Let suppose that the plank has an uniform density. The system is balanced if and only if its center of mass is located at O, which is determined by the following formula:

[tex]\bar x = \frac{(-0.25L)\cdot M+(0.25\cdot L)\cdot M}{2\cdot M}[/tex]

[tex]\bar x = 0[/tex]

Hence, the object is balanced as the center of mass of the system is located at O.

We kindly invite to check this question on center of mass: https://brainly.com/question/16698727

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