the resultant of two forces acting at an angle of 150 degree is10kgwt and is perpendicular to one of the forces, the magnitude of smaller force is
Answers
Given:
The resultant of two forces acting at an angle of 150 degree is10kgwt and is perpendicular to one of the forces
To find:
The magnitude of smaller force is
Solution:
Consider the attached figure and from given, we have,
P and Q are the forces and R is the resultant force.
|R| = 10 kg wt (given)
Now consider,
R = √(P² + Q² + 2PQ cos 150°)
⇒ 10 = √[P² + Q² + 2PQ (-√3/2)]
squaring on both the sides, we get,
100 = P² + Q² - √3PQ ...(1)
Again, we have,
Q² = P² + R²
100 = Q² - P² .....(2)
equating equations (1) and (2), we get,
P² + Q² - √3PQ = Q² - P²
2P² - √3PQ = 0
P(2P - √3Q) = 0
as P ≠ 0, ⇒ 2P - √3Q = 0
⇒ 2P = √3Q
∴ P = √3/2 Q
again using equation (2), we have,
100 = Q² - P²
100 = Q² - 3/4Q²
Q² = 400
∴ Q = 20
P = √3/2Q = √3/2 × 20 = 10√3
∴ P = 10√3
P is the smaller force with the value of 10√3