Balancing

You have been provided with a $24$ cm long stick with centimeter markings and four clay balls. Two of the clay balls $($call them A and $B)$ have the same mass, the third ball $(C)$ has twice the mass of ball $A,$ and the fourth ball $($D$)$ has three times the mass of ball $A.$

A$.$ Carefully push ball A and ball $B$ to separate ends of the stick so that the center of each ball is located at the end of the stick.

B$.$ Predict where you would need to place your finger so that you could balance the ball$-$and$-$stick unit on your finger. $($Ignore the mass of the stick itself.$)$ Discuss your reasoning with your partners. Record your prediction.

Check your prediction experimentally. Record your results.

C$.$ Replace ball $B$ with ball $C.$

Predict where you would need to place your finger so that you could balance the ball$-$and$-$stick unit on your finger. Be as specific as you can. $($For example, can you predict how many centimeters away from each ball you should place your finger?$)$

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Check your prediction experimentally. Record your results.

While balancing the ball$-$and$-$stick unit on one finger, how would you describe the relative distances between your finger and the center of each ball?