Physics Questions and Answers – Motion in a Plane – Resolution of Vectors

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This set of Physics Question Papers for NEET Exam focuses on “Motion in a Plane – Resolution of Vectors”.

1. The splitting of a vector into two component vectors is called ______
a) Vector resolution
b) Vector sum
c) Vector decomposition
d) Vector difference
View Answer

Answer: a
Explanation: The splitting of a vector into two component vectors is called vector resolution. The vector can be resolved into as many components as there are independent directions.
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2. What is the standard form for the resolution of a vector having magnitude ‘a’ and is inclined at an angle θ to the X axis?
a) a(cos θ î + sin θ ĵ)
b) a(sin θ î + cos θ ĵ)
c) a(sin θ î + sin θ ĵ)
d) a(cos θ î + cos θ ĵ)
View Answer

Answer: a
Explanation: The correct answer is a(cos θ î + sin θ ĵ). This is obtained by constructing a right-angled triangle with the distance of the point from the origin with either of the axes and then finding out the corresponding values for X and Y components.

3. What is the resolved form for a vector which is 5 units in long and is inclined at an angle of 45 degrees to the X axis?
a) \(\frac{1}{\sqrt{2}}\hat{i} + \frac{1}{\sqrt{2}}\hat{j}\)
b) \(\frac{5}{\sqrt{2}}\hat{i} + \frac{5}{\sqrt{2}}\hat{j}\)
c) \(\frac{5}{\sqrt{2}}\hat{i} + \frac{15}{\sqrt{2}}\hat{j}\)
d) \(\frac{10}{\sqrt{2}}\hat{i} + \frac{10}{\sqrt{2}}\hat{j}\)
View Answer

Answer: b
Explanation: The standard for is a(cos θ î + sin θ ĵ). Here, a = 5, and θ = 45 degrees. When we substitute this in the equation, we get, the resolved vector as \(\frac{5}{\sqrt{2}}\hat{i} + \frac{5}{\sqrt{2}}\hat{j}\).
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4. A velocity vector (5m/s) is making and angle of 60 degrees with X axis has a horizonal component of magnitude ___
a) 2.5
b) 5.5
c) 5
d)10/√3
View Answer

Answer: a
Explanation: The horizontal component of any vector with magnitude a is a cos θ. Here θ = 60. cos θ = ½. Hence the answer is 5/2 = 2.5 m/s.

5. A force vector (50 N) is making and angle of 30 degrees with X axis has a vertical component of magnitude ___
a) 25
b) 55
c) 50
d) 100/√3
View Answer

Answer: a
Explanation: The vertical component of any vector with magnitude a is a sin θ. Here θ = 60. sin θ = ½. Hence the answer is 50/2 = 25 N.
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6. A vector is represented as 4î + 3ĵ. What is its magnitude?
a) 5
b) 10
c) 4
d) 3
View Answer

Answer: a
Explanation: The magnitude of any vector can be found by taking the square root of sum of the squares of its two components. Hence, the sum of the squares of components is equal to 42 + 32 = 25. Square root of 25 = 5. Hence, the answer is 5.

7. A vector can be resolved along ______
a) Only one direction
b) Only two directions
c) Only three directions
d) Only in independent directions
View Answer

Answer: d
Explanation: A vector can be resolved in number of components. But, the number of components has to be equal to the number of independent directions available. It can only be resolved into independent directions no matter how many they are.
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