The maximum and minimum resultant of two vectors are in the ratio 4 : 3 . Then what is the ratio of their forces ?
A) 7 : 1
B) 1 : 5
C) 4 : 7
D) 3 : 7
Answers
AnswEr :
Option (A) is correct
Explanation :
The ratio of the maximum and minimum resultant forces is 4 : 3
To finD
The ratio of the forces
Law of Cosines
For the resultant force to be maximum,∅ = 0° (cos0 = 1)
For the resultant force to be minimum,∅ = 180° (cos180 = - 1)
We get the equations,
A + B = 4_______(1)
A - B = 3_______(2)
Adding equations (1) and (2),we get :
2A = 7
» A = 7/2
Putting A = 7/2 in (1),
(7/2) + B = 4
» - B = (-8 + 7)/2
» B = 1/2
Solving the above system of equations,
(A,B) = (7/2,1/2)
Ratio of A and B :
A : B = (7/2) : (1/2)
» A : B = 7/2 × 2/1
» A : B = 7 : 1
Answer:
Given:
Maximum and minimum resultant of 2 vectors are in the ratio of 4:3.
To find:
Ratio of forces
Concept:
Since ratio of resultant has been provided , lets consider x as the constant of proportionality.
So the maximum resultant will be 4x
The minimum resultant will be 3x
Calculation:
We should also remember that :
Max resultant is obtained when vectors are directed in the same direction.
Minimum resultant is obtained when vectors are directed in opposite direction .
Adding the 2 Equations , we get :
Putting value of vector a in 2nd equation :
Therefore ratio :