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The magnitude of two forces is such that when acting at right angels produce a resultant force of√ 20 and when acting at 60°produce a resultant equal to √28 find out the magnetude of two forces?

The magnitude of two forces is such that when acting at right angels produce a resultant force of√ 20 and when acting at 60°produce a resultant equal to √28 find out the magnetude of two forces?

Grade:12th pass

1 Answers

Sudhin Varghese
28 Points
2 years ago

R1 = √10 kg, θ1 = 90°,  R2 = √13 kg, θ2 = 60°

Let two forces are a1 and b2 (a12)

According to the problem:

CASE 1
 
√R1 = √a2 + b2
20  = a2 + b2 …......... (1)
 

CASE 2 

 
√R2 = √a2 + b2
28  =  a2 + b2+ 2 ab cos 60  ….................. (2)
 
Now,
 a2 + b2 = 20 from (1)
 
ab = 28 -20 = 8

So one is 2N and the other is 4 N

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