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The resultant of two forces 3P and 2P is R. If the first force is doubled then the resultant is also doubled. The angle between the two forces is
- a)60º
- b)120º
- c)70º
- d)180º
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The resultant of two forces 3P and 2P is R. If the first force is doub...
We can solve this problem using vector addition and the law of cosines. Let's assume that the angle between the two forces is θ.
The two forces can be represented as vectors:
F1 = 3P (along some direction)
F2 = 2P (making an angle θ with F1)
Their resultant R can be found by adding the two vectors:
R = F1 + F2
Now, if we double F1, the new resultant R' will be:
R' = 2F1 + F2
We are told that R' is twice as large as R:
R' = 2R
Substituting the expressions for R and R', we get:
2F1 + F2 = 2(F1 + F2)
Simplifying, we get:
F1 = F2
This means that the two forces are equal in magnitude.
Using the law of cosines, we can find the angle θ:
R^2 = F1^2 + F2^2 + 2F1F2cosθ
Substituting F1 = F2 = P, we get:
R^2 = 2P^2 + 2P^2cosθ
Rearranging and simplifying, we get:
cosθ = (R^2 - 4P^2) / (4P^2)
We know that cosθ = 1/2 (since the angle between the forces is such that doubling F1 doubles the resultant).
Substituting this value, we get:
1/2 = (R^2 - 4P^2) / (4P^2)
Solving for R/P, we get:
R/P = √3
Finally, using the law of sines, we can find the angle θ:
sinθ / R = sin(π/2 - θ) / P
Substituting R/P = √3, we get:
sinθ / √3P = cosθ / P
Substituting cosθ = 1/2, we get:
sinθ = √3/2
This means that the angle θ is 60 degrees.
Therefore, the answer is (a) 60.
The two forces can be represented as vectors:
F1 = 3P (along some direction)
F2 = 2P (making an angle θ with F1)
Their resultant R can be found by adding the two vectors:
R = F1 + F2
Now, if we double F1, the new resultant R' will be:
R' = 2F1 + F2
We are told that R' is twice as large as R:
R' = 2R
Substituting the expressions for R and R', we get:
2F1 + F2 = 2(F1 + F2)
Simplifying, we get:
F1 = F2
This means that the two forces are equal in magnitude.
Using the law of cosines, we can find the angle θ:
R^2 = F1^2 + F2^2 + 2F1F2cosθ
Substituting F1 = F2 = P, we get:
R^2 = 2P^2 + 2P^2cosθ
Rearranging and simplifying, we get:
cosθ = (R^2 - 4P^2) / (4P^2)
We know that cosθ = 1/2 (since the angle between the forces is such that doubling F1 doubles the resultant).
Substituting this value, we get:
1/2 = (R^2 - 4P^2) / (4P^2)
Solving for R/P, we get:
R/P = √3
Finally, using the law of sines, we can find the angle θ:
sinθ / R = sin(π/2 - θ) / P
Substituting R/P = √3, we get:
sinθ / √3P = cosθ / P
Substituting cosθ = 1/2, we get:
sinθ = √3/2
This means that the angle θ is 60 degrees.
Therefore, the answer is (a) 60.
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Community Answer
The resultant of two forces 3P and 2P is R. If the first force is doub...
C vector = A vector + B vector
Let angle b/w the 2 forces be x.
Now , ATQ...
C vector = under root ( A^2 + B^2 + 2 × A
vector × B vector).
or, C= under root ( 9P^2 + 4P^2 + 2 × A vector × B vector)
Now , 2C= under root ( 36P^2 + 4P^2 + 4 × A vector × B vector)
As , A is doubled , C also gets doubled.
So, ATQ...
under root( 36P^2 + 16 P^2 + 8 × A vector × B vector) = under root( 36P^2 + 4 P^2 + 4 × A vector × B vector)
or, 4 × A vector × B vector = -- 12 P^2
or, 4 A B cos x = -- 12 P^2
or, 24 P^2 cos x = -- 12 P^2
Therefore , cos x = -- 1/2 ..... so x = 2pi/3= 120 degrees..
Hope it helps!!!
Let angle b/w the 2 forces be x.
Now , ATQ...
C vector = under root ( A^2 + B^2 + 2 × A
vector × B vector).
or, C= under root ( 9P^2 + 4P^2 + 2 × A vector × B vector)
Now , 2C= under root ( 36P^2 + 4P^2 + 4 × A vector × B vector)
As , A is doubled , C also gets doubled.
So, ATQ...
under root( 36P^2 + 16 P^2 + 8 × A vector × B vector) = under root( 36P^2 + 4 P^2 + 4 × A vector × B vector)
or, 4 × A vector × B vector = -- 12 P^2
or, 4 A B cos x = -- 12 P^2
or, 24 P^2 cos x = -- 12 P^2
Therefore , cos x = -- 1/2 ..... so x = 2pi/3= 120 degrees..
Hope it helps!!!
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The resultant of two forces 3P and 2P is R. If the first force is doubled then the resultant is also doubled. The angle between the two forces isa)60ºb)120ºc)70ºd)180ºCorrect answer is option 'B'. Can you explain this answer?
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The resultant of two forces 3P and 2P is R. If the first force is doubled then the resultant is also doubled. The angle between the two forces isa)60ºb)120ºc)70ºd)180ºCorrect answer is option 'B'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The resultant of two forces 3P and 2P is R. If the first force is doubled then the resultant is also doubled. The angle between the two forces isa)60ºb)120ºc)70ºd)180ºCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The resultant of two forces 3P and 2P is R. If the first force is doubled then the resultant is also doubled. The angle between the two forces isa)60ºb)120ºc)70ºd)180ºCorrect answer is option 'B'. Can you explain this answer?.
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