question_answer

The resultant of two forces P N and 3 N is a force of 7 N. If the direction of the 3 N force were reversed, the resultant would be \[\sqrt{19}N\]. The value of P is       AIEEE  Solved  Paper-2007

A)  5 N    

B)         6 N       

C)         3 N       

D)         4 N

Correct Answer: A

Solution :

                \[{{7}^{2}}={{P}^{2}}+{{3}^{2}}+2\times 3\times p\cos \theta \]           ... (i) and\[{{(\sqrt{19})}^{2}}={{p}^{2}}+{{(-3)}^{2}}+2\times (-3)\times p\cos \theta \]...(ii) On adding Eqs. (i) and (ii), we get \[68\,=2{{P}^{2}}\,+18\Rightarrow P=5\]