The magnitude of 4 pairs of displacement vectors r given.which pairs of displacement vectors cannot be added to give a resultant vector of magnitude 4 cm
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your question is incomplete .
A complete question is -------> The magnitudes of four pairs of displacement vectors are given. Which pairs of displacement vectors cannot be added to give a resultant vector of magnitude 4 cm?
Choose the correct answer(s)
(a) 2 cm, 3 cm
(b) 1 cm, 3 cm
(c) 1 cm, 5 cm
(d) 1 cm, 7 cm
Solution :- Resultant R of two vectors A and B is given by
R = √{A² + B² + 2AB cosФ}
Where Ф is angle between A and B.
Maximum value of R , when Ф = 0°
e.g., R = √{A² + B² + 2AB} = |A + B|
And minimum value of R , when Ф = 180°
e.g., R = √{A² + B² - 2AB} = |A - B|
Means, |A - B| ≤ R ≤ |A + B|
Hence, resultant of any two vectors {A, B} is lies between |A - B| and |A + B|
Now, check options
option (A) :- A = 2cm and B = 3cm
|A - B| = |2 - 3| = 1
|A + B| = |2 + 3 | = 5
Hence, 1 ≤ R ≤ 5 so, the R = 4 is possible
Similarly, option (B), (C) is possible
Now, check option (D)
|A - B| = |1 - 7| = 6
|A +B| = |1 + 7| = 8
hence, 6 ≤ R ≤ 8 so, R ≠ 4 .
Hence, option (D) 1cm , 7cm can't give resultant vector of magnitude 4cm
your question is incomplete .
A complete question is -------> The magnitudes of four pairs of displacement vectors are given. Which pairs of displacement vectors cannot be added to give a resultant vector of magnitude 4 cm?
Choose the correct answer(s)
(a) 2 cm, 3 cm
(b) 1 cm, 3 cm
(c) 1 cm, 5 cm
(d) 1 cm, 7 cm
Solution :- Resultant R of two vectors A and B is given by
R = √{A² + B² + 2AB cosФ}
Where Ф is angle between A and B.
Maximum value of R , when Ф = 0°
e.g., R = √{A² + B² + 2AB} = |A + B|
And minimum value of R , when Ф = 180°
e.g., R = √{A² + B² - 2AB} = |A - B|
Means, |A - B| ≤ R ≤ |A + B|
Hence, resultant of any two vectors {A, B} is lies between |A - B| and |A + B|
Now, check options
option (A) :- A = 2cm and B = 3cm
|A - B| = |2 - 3| = 1
|A + B| = |2 + 3 | = 5
Hence, 1 ≤ R ≤ 5 so, the R = 4 is possible
Similarly, option (B), (C) is possible
Now, check option (D)
|A - B| = |1 - 7| = 6
|A +B| = |1 + 7| = 8
hence, 6 ≤ R ≤ 8 so, R ≠ 4 .
Hence, option (D) 1cm , 7cm can't give resultant vector of magnitude 4cm
Answered by
10
Answer:
A similar type of situation in this question-
Which of the following pair of displacement cannot be added to produce a resultant displacement of 2m?
(1) 1m and 1m
(2) 1m and 2m
(3) 1m and 3m
(4) 1m and 4m
Explanation:
Maximum value of R= mod A+B
Minimum value of R= mod A-B
Therefore, from first option,
Rmax=2m
Rmin=0m
From second option,
Rmax=3m
Rmin=1m
2 is included in between.
From third option,
Rmax=4m
Rmin=2m
From fourth option,
Rmax=5m
Rmin=3m
2 is not included in between.
Hence, option (4) is correct.
Hope it will help you
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