Q1: Two parallel forces 20 kg and 15 kg act. In order that the distance of the resultant from 20 kg force may be the same as that of the former resultant was from 15 kg, the 20 kg force is diminished by

ANS:C - 8.75 kg

Given:

• Two parallel forces are 20 kg and 15 kg.
• The condition is to adjust the 20 kg force so that the distance of the resultant from the 20 kg force is the same as the distance from the 15 kg force.

We denote the distance of the resultant from the 20 kg force as d1​ and from the 15 kg force as d2​. According to the conditions provided, we have: d1​=d2​ Now, the principle of moments states that the moment of the resultant force about any point is equal to the algebraic sum of the moments of the components about the same point. Let's assume that the distance of the resultant from the 20 kg force is d1​. Then, the moment of the 20 kg force about the resultant is R1​×d1​. Similarly, the moment of the 15 kg force about the resultant is R2​×d2​. According to the principle of moments, we have: R1​×d1​=R2​×d2​ Given that d1​=d2​, we can rewrite the equation as: R1​=R2​ This means that the magnitude of the resultant force is the same for both setups. For the original setup, the magnitude of the resultant force is R1​=20 kg. To diminish the 20 kg force to a new magnitude, we need to find the difference between the original magnitude and the new magnitude: Difference=20 kg−New MagnitudeDifference=20kg−New Magnitude Now, since the new magnitude of the resultant force is the same as the original, we know that the new magnitude of the 20 kg force will be equal to the original magnitude of the 15 kg force, which is 15 kg. New Magnitude=15 kgNew Magnitude=15kg Therefore, Difference=20 kg−15 kg=5 kg  Thus, the 20 kg force needs to be diminished by 5 kg. So, the correct deduction should be 5 kg, not 8.75 kg. The calculation of 8.75 kg is incorrect in the context of the problem and the principles of equilibrium.