Balaning metre-stick - Find the mass

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A metre-stick balances at the 49.7 cm mark, and when a 50g mass is added at the 10 cm mark, the fulcrum shifts to 39.2 cm for balance. The center of gravity of the stick is at 29.7 cm, but this value needs to be corrected to 49.7 cm for accurate calculations. To find the mass of the stick, consider it as a point mass at the 49.7 cm mark and apply the equilibrium condition m1g*d1 = m2g*d2, where d1 and d2 are the distances from the pivot. The discussion highlights the importance of correctly identifying the pivot point and distances to solve for the mass of the metre-stick.
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3) a metre-stick is found to balance at the 49.7cm mark when placed on a fulcrum, when a 50g mass is attached at the 10cm mark the fulcrum must be moved to the 39.2 cm mark for balance. what is the mass of the meter stick?

- just plain stuck on this, tried about 3 different ways of attempting the question, but couldn't find one that suited! anyone got any ideas on how to start it?? again, any help appreciated!

:)
 
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The center of gravity of the stick is at 29.7cm mark, its mass to be considerd at this point, but the rest part is not appearing correct. It will not get balanced in second situation. Check the numerical values given.
 
Last edited:
mukundpa said:
The center of gravity of the stick is at 29.7cm mark, its mass to be considerd at this point, but the rest part is not appearing correct. It will not get balanced in second situation. Check the numerical values given.

yes sorry, you're right... it was meant to read 49.7cm, which i have now changed! sorry! i have still been trying to do it, found a number of various formulas and ways to go about it on the net, but none are helping me to find the mass of the stick, rather the masses of the objects joined to the stick...
 
Consider the meter stick as a point mass at the 49.7cm mark. Then on the left you have the 50g point mass at a distance d1 = (39.2 - 10)cm from the pivot and on the right you have the c.m. of the stick at a distance d2 = (49.7 - 39.2)cm from the pivot.
So just use the equilibrium condition m_1gd_1 = m_2gd_2
 

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