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Welcome to the CPL Performance question and answer forum. Please feel free to post your questions but more importantly also suggest answers for your forum colleagues. Bob himself or one of the other tutors will get to your question as soon as we can.
I'm confused with my answer and the answer from the book. It's because from my calculation, 37.93088 kg is to be added to the rear compartment. It has been rounded up to 38 kg but the CG will be at 2680.0606 mm which should be considered imbalance. Therefore, should be answer be 37 kg?
If the ballast required is 37.9kg then 37kg would not be enough. Also, I'm pretty sure the marking system in the exam would have sensible margins applied for full marks to be allocated. Unless you have a set of scales calibrated to 100,000th of a Kilo, it does seem a bit of an academic argument. After all, there is only one spot on the floor of the rear compartment where the arm is exactly 5000mm from the datum. So, unless the weight is placed precisely at that point the calculated answer is invalid anyway.