Answer:
For the scale to balance, the total of torques on either side of the scale must be equal. Assigning the numbers 1, 2, and 3 to the weights of 5kg, 6kg, and the "?" weight, respectively, we have our torque equation: T1 + T2 = T3.
Each torque is by definition T = W x L, where W is the weight and L is the distance from the fulcrum. Recall that W = M x g, where M is the mass and g is the gravitational constant.
M1 x g x L1 + M2 x g x L2 = M3 x g x L3
We can simplify by dividing both sides by g:
M1 x L1 + M2 x L2 = M3 x L3
Our givens are M1 = 5kg, L1 = 12cm, M2 = 6kg, L2 = 15cm, M3 = ?, L3 = 20cm. Substituting the values given in the question in the equation:
5kg x 12cm + 6kg x 15cm = M3 x 20cm
Now solve like a regular equation (multiplying before adding and isolating M3), just do not forget to mind the units as well:
(5 x 12) [kg x cm] + (6 x 15) [kg x cm] = M3 x 20cm
Multiply the figures on the left side:
60 [kg x cm] + 90 [kg x cm] = M3 x 20cm
Add the figures on the left side:
150 [kg x cm] = M3 x 20cm
Divide by 20cm to isolate M3:
M3 = 150 [ kg x cm] / 20cm
M3 = (150/20) [kg x cm / cm]
=> M3 = 7.5kg
Therefore, 7.5 kg is the correct answer.