Question

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​

Answer 1

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