Physics · Kinematics · chapter 3 of 14

Class 11 Physics Chapter 3: Motion in a Plane MCQs with answers

10 multiple-choice questions on Motion in a Plane, each with its answer and the reason, written from the NCERT chapter. For school exams on the CBSE pattern, JEE Main and NEET, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter.

Question 1
Vector P has magnitude 5 units and points due north. Vector Q has magnitude 5 units and points north-east. Which statement is correct?
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Answer: (b) P ≠ Q, since their directions differ

Two vectors are equal only if they have the same magnitude and the same direction. P and Q have equal magnitudes but different directions, so P ≠ Q.

Question 2
A vector A of magnitude 4 units points due east. The vector −2.5A has
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Answer: (d) magnitude 10 units, pointing west

Multiplying by a negative number −λ reverses the direction and multiplies the magnitude by λ: |−2.5A| = 2.5 × 4 = 10 units, pointing west.

Question 3
The unit vector along A = 3î − 4ĵ is
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Answer: (a) (3î − 4ĵ)/5

n̂ = A/|A|, and |A| = √(3² + 4²) = 5, so n̂ = (3î − 4ĵ)/5. Dividing by 25 uses |A|², and 7 adds the components instead of using Pythagoras.

Question 4
A force of 20 N acts in the x-y plane at 150° to the +x-axis. Its x-component, in newtons, is
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Answer: (c) −10√3

Ax = A cos θ = 20 cos 150° = 20 × (−√3/2) = −10√3 N. The component is negative because the force points to the left of the y-axis; −10 is A sin θ with the wrong sign.

Question 5
If A = 2î + 3ĵ and B = −5î + ĵ, the magnitude of A + B is
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Answer: (c) 5

Rx = 2 + (−5) = −3, Ry = 3 + 1 = 4, so |R| = √(9 + 16) = 5. √53 is |A − B|, and 7 adds the magnitudes of the components.

Question 6
A car goes round a hairpin bend on a hill road. At any instant, the direction of its velocity is
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Answer: (b) along the tangent to its path, in the direction of motion

Velocity is the limit of Δr/Δt as Δt → 0; in this limit Δr lies along the tangent, so the velocity is tangent to the path at that point, in the direction of motion.

Question 7
For an object moving in a plane, the angle between its velocity and its acceleration
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Answer: (c) can have any value from 0° to 180°

Only in one dimension are velocity and acceleration along one line. In two or three dimensions the angle between them may be anything from 0° to 180°.

Question 8
A stone is thrown at an angle to the horizontal. Air resistance is negligible. Which quantity stays constant throughout its flight?
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Answer: (d) the horizontal component of its velocity

The only acceleration is g, vertically downward, so ax = 0 and vx = v₀ cos θ₀ stays constant. The vertical component changes at the rate g, so the speed and the velocity change too.

Question 9
A cyclist rides round a circular track at a steady speed. Her acceleration is
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Answer: (a) of constant magnitude, always directed towards the centre, so it is not a constant vector

The velocity keeps changing direction, so there is an acceleration, v²/R, towards the centre. Its magnitude is constant but its direction turns with her, so it is not a constant vector.

Question 10
A disc rotates about its axis with constant angular speed. Points A and B are 5 cm and 15 cm from the axis. The ratio of their linear speeds vA : vB is
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Answer: (d) 1 : 3

Every point of the disc has the same ω, and v = Rω, so vA : vB = 5 : 15 = 1 : 3. 1 : 1 would be the ratio of angular speeds; 1 : 9 wrongly squares the ratio of the radii.

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