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  • The sum of magnitudes of two forces acting at the point is 16N. If the resultant force is 8N and its direction is perpendicular to smaller force, then the forces are,<div class='qna-o

The sum of magnitudes of two forces acting at the point is 16N. If the resultant force is 8N and its direction is perpendicular to smaller force, then the forces are,

Option: 1

6N and 10N


Option: 2

8N and 8N


Option: 3

4N and 12N

 


Option: 4

2N and 14N


Answers (1)

best_answer

Given, A+B=16

\tan \alpha =\frac{B\sin \theta }{A+B\cos \theta }=\tan {{90}^{\circ }}

Thus, 

\\A+B\cos \theta =0 \\ \\\cos \theta =\frac{-A}{B} \\

We also have , 

8=\sqrt{{{A}^{2}}+{{B}^{2}}+2AB\cos \theta }\; \; \; \; \; \; .......(2)

Solving equation (1) and (2), we get A=6N  and B=10N.

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Sayak

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