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For two equal non parallel forces acting a a point the square of resultant is 3 times the product of forces, what is angle between forces

For two equal non parallel forces acting a a point the square of resultant is 3 times the product of forces, what is angle between forces

Grade:11

2 Answers

Arun
25763 Points
3 years ago

Given two forces and Q, such that | P | = P, | Q | = Q, and P = Q, acting at a point, such that square of magnitude R of resultant R of and is 3 P² = 3 Q². We are required to find the angle between and Q.

Let the angle between and Q is ∅. Then by parallelogram law of vectors we have for the resultant, that,

R² = P² + Q² + 2 P Q Cos ∅ = P² + P² + 2 P P Cos ∅= 2 P² + 2 P² Cos ∅. ……..(1)

We are given that R² = 3 P². Substituting for R² in equation 1, we get,

3 P² = 2 P² + 2 P² Cos ∅, or Cos ∅ = ½ or ∅ = 60° .

The angle between the two forces is 60° 

Shailendra Kumar Sharma
188 Points
3 years ago
Assume the Force be A, B and resultant be C
Given C2=A2+B2+2ABCOS(THETA)
GIVEN A=B
SO C2=2A2+2A2COS(THETA)
NOW C2=3A2
SO 3A2=2A2+2A2COS(tHETA)
S Cos(theta)=1/2
SO ANGLE WILL BE 60 DEGREE

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