Two forces equal to P and 2P newton act on a particle . If the first be doubled and the second be increased by 20 newton, the direction of the resultant is unaltered . Find the value of P .

Two forces equal to P and 2P newton act on a particle . If the first b

1.	Two forces equal to P and 2P newton act on a particle . If the first be doubled and the second be increased by 20 newton, the direction of the resultant is unaltered . Find the value of P .
Answer» <html><body><p><<a href="https://interviewquestions.tuteehub.com/tag/p-588962" style="font-weight:bold;" target="_blank" title="Click to know more about P">P</a>></p>Solution :Let the resultant make angle `beta`with the force P .<br/>`:.`In <a href="https://interviewquestions.tuteehub.com/tag/first-461760" style="font-weight:bold;" target="_blank" title="Click to know more about FIRST">FIRST</a> case,<br/>`tan beta = (<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a> P sin theta)/( P + 2 P cos theta)`<br/>In second case,<br/>`tan beta = ((2P + 20) sin theta)/(2P + (2P + 20) cos theta)`<br/><a href="https://interviewquestions.tuteehub.com/tag/hence-484344" style="font-weight:bold;" target="_blank" title="Click to know more about HENCE">HENCE</a>,<br/>`((2P + 20) sin theta)/( 2 P + (2P + 20) cos theta) = (2P sin theta)/(P + 2 P cos theta)`<br/>(or)`(2P sin theta)/( P +2 P cos theta) = (2 0 sin theta)/( P + 2 0 cos theta)`[`:' (a)/(b) = (c)/(d) = (a-c)/(b-d)` ]<br/>From the above <a href="https://interviewquestions.tuteehub.com/tag/equation-974081" style="font-weight:bold;" target="_blank" title="Click to know more about EQUATION">EQUATION</a> , 2P = 20<br/>(or) P = 10 N</body></html>