Question 5 of 12 ncorrect Map sapling learning While on a camping trip, you woul

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Question 5 of 12 ncorrect Map sapling learning While on a camping trip, you would like to carry water from the lake to your campsite. You have two non identical buckets which you attach to a 1.35 m long rod. Since the buckets are not identical, you find that the rod balances about a point 0.0127 m 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? 0.0127 m O bucket 2 o hey hold the same amount of water o bucket 1 Fill in the blank: The heavier bucket contains more water than the lighter bucket does Number 6.2413 There is a hint available! View the hin bottom divider bar. Click on the divider bar again to hide the hint.

Explanation / Answer

Let m1 and m2 be the mass of water contained in bucket 1 and 2 respectively

Distance of bucket 1 from pivot, r1 = (1.35/2) - 0.0127 = 0.6623 m

Distance of bucket 2 from pivot, r2 = (1.35/2) + 0.0127 = 0.6877 m

Torque due to a force F is given as , torque = F*r*sin(theta) where theta is angle between r and F

Torque is taken to be positive if the rod tends to rotate anti clock-wise and negative if rotation is expected clock-wise.

Since the rod is in equilibrium, hence total torque about the pivot must be zero.

That is   m1*g*r1 sin90 - m2*g*r2 sin90 = 0 => m1*r1 = m2*r2 => m1/m2= r2/r1 = 1.0383512

Hence, m1 = 1.0383512 m2  

Implies that m1 > m2  

% = (m1 - m2)*100/m2 = (1.0383512 -1)m2*100/m2 = 3.835%

So, the bucket 1 has 3.835% more water than bucket 2

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