Two forces are in the ratio of 7 5 The maximum and minimum of their resultants are in the ratio of

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Maximum and minimum resultant of two forces are in the ratio 5: 2 then the ratio of the forces is what

Solution

Let A and B be the 2 forces. since force is a vector maximum force is the summation of 2 forces ie when both forces are in the same direction. So maxi Force= F1+ F2 Similarly minimum force is when both forces act in opposite direction. So mini force = F1-F2 Given ratio of maxi to mini resultant force is 5:2. ie (F1+F2) ÷ (F1-F2)= 5÷2 We need to find F1/F2. So Cross multiply 2×(F1+F2) = 5×(F1-F2) 2F1+ 2F2 =5F1-5F2 7F2 = 3F1 F1/F2=7/3