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The 14 long stick has a mass of 4 kg placed at one end and a mass of 16 kg placed at the other. When the stick is balanced by placing it on a fulcrum each of the masses exerts a torque that rotates the stick about the point where the fulcrum is. To keep the stick balanced, the torque exerted by each of the masses should cancel.
Let the point where the fulcrum should be placed be at a distance L from the end where the 4 kg mass is placed.
The torque due to the 4 kg mass is 4*9.8*L. The distance of the 16 kg mass from the fulcrum is 14 - L. The torque on the stick due to the 16 kg mass is 16*9.8*(14 - L). This torque is in the opposite direction as that exerted by the 4 kg mass.
Equating the two torques:
4*9.8*L = 16*9.8*(14 - L)
=> 4L = 224 - 16L
=> L = 224/20
=> L = 11.2
The center of gravity of the stick is at a point 11.2 meters from the end that has the 4 kg mass. If the fulcrum is placed below this point, the stick will remain balanced.
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