I\'m certain that bucket one holds more water but I\'m not sure of the percentag

Question

I'm certain that bucket one holds more water but I'm not sure of the percentage.

While on a camping trip, you would like to carry water from the lake to your campsite. You have two nonidentical buckets which you attach to a 1.27 m long rod. Since the buckets are not identical, you find that the rod balances about a point 2.23 cm from its midpoint, as shown below. The weight of the rod and empty buckets are negligible compared to the weight of the water. Which bucket holds more water? Fill in the blank: The heavier bucket contains % more water than the lighter bucket.

Explanation / Answer

Since the center of mass shifts towards the heavier mass side,then the bucket on the right has more weight than the left

So the answer is bucket 2

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let m1 be the mass of the water in bucket 1

and similarly m2 be the mass of water in bucket 2

Xcm = ((m1*x1)+(m2*x2))/(m1+m2)

(1.27/2)+(0.0223) = (m2*1.27)/(m1+m2)

0.6573 = (m2*1.27)/(m1+m2)

(m1+m2)/(m1*1.27) = 0.6573

(1/1.27)+(m2/(m1*1.27)) = 0.6573

m2/(m1*1.27) = 0.6573-(1/1.27) =-0.13

m2 = 0.1651*m1

So the answer is The heavier bucket contains 16.5 % more water than the lighter bucket

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