Free Addition of Vectors MCQs with Answers

• A. 1 N
• B. 5 N
• C. 7 N
• D. 12 N

Explanation: For perpendicular vectors the resultant is the square root of (3 squared plus 4 squared), which is the square root of 25, giving 5 N.

• A. 2F
• B. F times the square root of 3
• C. F
• D. zero

Explanation: Using the parallelogram rule, the resultant is the square root of (F squared plus F squared plus 2F squared cos 120), and since cos 120 is…

• A. one
• B. two
• C. three
• D. four

Explanation: Two unequal forces can never cancel, since cancelling requires equal magnitudes in opposite directions.

• A. the vector sum of all forces acting on the body is zero
• B. the sum of all torques about any point is zero
• C. the body is at rest
• D. no force acts on the body at all

Explanation: With zero net force there is no acceleration of the centre of mass, which is translational equilibrium.

• A. its mass is very small
• B. the net force is zero but the net torque is not
• C. the forces are all vertical
• D. it is moving at constant speed

Explanation: Two equal and opposite forces acting along different lines form a couple: they cancel as vectors, so there is no acceleration, but they…

• A. 90 degrees
• B. 180 degrees
• C. 120 degrees
• D. 0 degrees

Explanation: Parallel vectors add directly, so the resultant equals the sum of the magnitudes, which is the largest value achievable.

• A. along the ladder
• B. vertically upwards
• C. perpendicular to the wall
• D. parallel to the wall

Explanation: A smooth surface can exert no friction, so the only force it can apply is the normal reaction, which by definition acts at right angles to…

• A. lie along one straight line
• B. form a closed triangle
• C. all be equal in magnitude
• D. be mutually perpendicular

Explanation: A zero resultant means the head of the last vector coincides with the tail of the first, so the three vectors close a triangle.

• A. 90°
• B. 180°
• C. 270°
• D. None of these

Explanation: Anti-parallel vectors lie along the same line but point in opposite directions, so the angle between them is 180°.

• A. A resultant vector
• B. A unit vector
• C. A null vector
• D. A position vector

Explanation: A vector with magnitude exactly one is called a unit vector, and it is used to specify direction.

• A. Addition of vectors
• B. Subtraction of vectors
• C. Multiplication of vectors
• D. Resolution of vectors

Explanation: Composition combines vectors to find their resultant, whereas resolution separates one vector into rectangular components.

• A. Zero
• B. Two
• C. Three
• D. None

Explanation: Two unequal vectors cannot have a zero resultant because their magnitudes would have to be equal and opposite.

• A. 2N & 5N
• B. 20N & 2N
• C. 3N & 6N
• D. 4N & 1N

Explanation: The resultant of two vectors with magnitudes 3 N and 6 N can range from |6 N - 3 N| = 3 N to 6 N + 3 N = 9 N, so 8 N is possible.

• A. 18N
• B. 22N
• C. 25N
• D. 30N

Explanation: For vectors of 10 N and 15 N, the resultant must lie between |15 N - 10 N| = 5 N and 15 N + 10 N = 25 N.

• A. Magnitude
• B. Velocity
• C. Direction of vector
• D. Frequency

Explanation: A unit vector has magnitude 1 and is used mainly to specify direction, such as i, j and k along coordinate axes.

• A. 1
• B. 2
• C. 3
• D. 4

Explanation: Physical quantities are commonly divided into two categories: scalars, which have magnitude only, and vectors, which have both magnitude…

• A. Rotational equilibrium
• B. Translational equilibrium
• C. Static equilibrium
• D. Both A and C are corret answer

Explanation: Static equilibrium means the body is at rest, whereas dynamic equilibrium involves uniform motion with zero resultant force and, where…

• A. 1st condition of equilibrium
• B. 2nd condition of equilibrium
• C. Both Ist and 2nd condition of equilibrium
• D. Impossible

Explanation: Complete equilibrium requires both translational equilibrium, with the resultant force equal to 0 N, and rotational equilibrium, with the…

• A. Always at rest
• B. Always in uniform motion
• C. May be at rest or in uniform motion
• D. May be at rest or in motion

Explanation: When the resultant force and resultant torque are zero, a body has no acceleration and can either remain at rest or continue with constant…

• A. ??3 i^ + ??3 j^ + ??3 k^
• B. 1/??3 i^ + 1/??3 j^ +1/ ??3 k^
• C. ??3 / 3 i^ + ??3 / 3 j^ + ??3 / 3 k^
• D. Both B and C are correct

Explanation: Assuming the damaged symbols represent square roots, the vector in b has magnitude √[(1/√3)² + (1/√3)² + (1/√3)²] = √(3 x 1/3) = 1, so it…