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Grade 12th passMechanics

When two forces of magnitude P and Q are perpendicular to each other, their resultant is of magnitude R. When they are at an angle of 180 degrees to each other, their resultant is of magnitude R/root 2. Find the ratio of P and Q.

Profile image of Shreya Gautam
8 Years agoGrade 12th pass
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1 Answer

Profile image of Arun
ApprovedApproved Tutor Answer8 Years ago
Dear student
 
R² = P² + Q² + 2PQ cos 90°
R² = P² +Q²
Now
R²/2 = P² + Q² -2PQ
P-Q = R/sqrt(2)      ......(i)
R² /2 = R² - 2PQ
R² = 4PQ
(P+Q)² = P² + Q² + 2PQ = R² + R²/2
P+Q = sqrt3 * R/sqrt (2)       .....(ii)
Solve equation 1 and 2
And then find P and Q , then you will be able to find the ratio.