Motion in a PlaneNEET MCQs with solutions
Motion in a Plane covers vectors, projectile motion and uniform circular motion. NEET tests projectile formulas (range, max height, time of flight), vector addition/resolution and centripetal acceleration. Projectile motion numericals and vector-based problems are NEET staples.
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- 11 Physics
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- 313 questions
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Practise 24 questions
Tap an option to check it. Questions from every NCERT topic in this chapter, from easy to hard.
Q1Grand Test
A vector has components 12î and 5ĵ. Its magnitude is:
Not quite — the answer is D.
|A| = √(12²+5²) = √(144+25) = √169 = 13 units. Option C (17) is the trap — it comes from adding 12+5 directly instead of using the Pythagorean theorem.
Q2Grand Test
Two vectors of magnitudes 6 units and 8 units are inclined at 60°. Their resultant magnitude is:
Not quite — the answer is C.
R = √(36+64+2×6×8×cos60°) = √(100+48) = √148 = 2√37 units. Option A (10) is the trap — it assumes perpendicular vectors, using R = √(6²+8²) without the cosine term.
Q3Grand Test
Vectors A = 4î+3ĵ and B = 3î−4ĵ. The angle between them is:
Not quite — the answer is B.
A·B = (4)(3)+(3)(−4) = 12−12 = 0. Zero dot product means vectors are perpendicular, so angle = 90°. Option A (0°) is the trap — students see similar-looking components and assume parallel vectors.
Q4Scalars and Vectors
Which of the following is a scalar quantity?
Not quite — the answer is B.
Distance has magnitude only, with no associated direction. Displacement, velocity, and acceleration all require both magnitude and direction to be fully described.
Q5Scalars and Vectors
Which of the following is a vector quantity?
Not quite — the answer is C.
Force has both magnitude and direction, making it a vector. Mass, temperature, and energy are fully described by magnitude alone and are therefore scalars.
Q6Scalars and Vectors
A particle travels 12 m east and then 5 m west along a straight line. Its displacement is:
Not quite — the answer is A.
Displacement = net change in position = 12 − 5 = 7 m east. The common error is adding both distances to get 17 m, which gives total path length (distance), not displacement.
Q7Vector Algebra (Addition, Subtraction, Resolution)
According to the triangle law of vector addition, two vectors are represented by two sides of a triangle taken in order. The resultant is represented by:
Not quite — the answer is B.
Triangle law states the resultant is the third side taken in opposite order (tail of first to head of second). Option A wrongly links resultant to the larger vector, which is a common misread of the law.
Q8Vector Algebra (Addition, Subtraction, Resolution)
If two vectors of magnitudes 6 units and 8 units act in the same direction, the magnitude of the resultant is:
Not quite — the answer is C.
Vectors in the same direction add directly: 6 + 8 = 14 units. Option A (2 units) is the minimum resultant (opposite direction). Option D (48) is their product, not sum.
Q9Vector Algebra (Addition, Subtraction, Resolution)
Two vectors of magnitudes 10 N and 6 N act in opposite directions. Their resultant magnitude and direction are:
Not quite — the answer is A.
Opposite vectors: resultant = 10 - 6 = 4 N, directed along the larger (10 N) vector. Option B wrongly assigns direction to the smaller vector. Option C adds instead of subtracts.
Q10Projectile Motion
A projectile is launched with initial speed u at angle θ to the horizontal. The horizontal component of its velocity is:
Not quite — the answer is B.
Horizontal component uₓ = u cosθ since θ is measured from horizontal. Option A (u sinθ) is the vertical component — a common sin/cos swap. cos gives the adjacent side to angle θ in the velocity triangle.
Q11Projectile Motion
A projectile is fired with speed 20 m/s at 30° to the horizontal. Its initial vertical component of velocity is: (g = 10 m/s²)
Not quite — the answer is A.
uᵧ = u sin30° = 20 × 0.5 = 10 m/s. Option B (10√3 m/s) is u cos30°, the horizontal component — the classic sin/cos confusion trap. sin gives the side opposite to θ.
Q12Projectile Motion
Which physical quantity remains constant throughout the motion of a projectile (neglecting air resistance)?
Not quite — the answer is D.
Horizontal acceleration is zero throughout, so horizontal velocity is unchanged. Vertical velocity changes due to g; speed changes as direction changes. Option C (vertical acceleration) is also constant, but vertical acceleration is not a component of velocity — the question asks for a velocity quantity.
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Get RankUp on Google PlayQ13Mixed Revision
A vector has components 6î and 8ĵ. Its magnitude is:
Not quite — the answer is A.
|A| = √(6² + 8²) = √100 = 10 units. Options B and C arise from adding components directly instead of using the Pythagorean theorem.
Q14Mixed Revision
Two vectors of magnitudes 5 units and 12 units are perpendicular. Their resultant magnitude is:
Not quite — the answer is C.
R = √(5² + 12²) = √169 = 13 units. Option D (17) is the trap — it results from simple addition of magnitudes, valid only for parallel vectors.
Q15Mixed Revision
A projectile is projected with speed 20 m/s at 30°. Taking g = 10 m/s², its time of flight is:
Not quite — the answer is B.
T = 2u sinθ/g = 2×20×0.5/10 = 2 s. Option A (1 s) comes from omitting the factor of 2, i.e., computing only ascent time.
Q16Uniform Circular Motion
A particle moving with constant speed in a circular path undergoes:
Not quite — the answer is C.
Speed is constant but direction of velocity changes, so acceleration exists. This centripetal acceleration points toward the centre and is constant in magnitude. Option B (constant velocity) is wrong because velocity direction changes; Option D confuses centripetal with tangential acceleration.
Q17Uniform Circular Motion
The direction of the instantaneous velocity of a particle in uniform circular motion is:
Not quite — the answer is B.
Velocity is always directed along the tangent to the path at every instant. Option A (toward centre) is the direction of centripetal acceleration, not velocity. Option C (radially outward) is the direction of no physical vector in UCM.
Q18Uniform Circular Motion
A particle moves in a circle of radius 5 m with angular velocity 4 rad/s. Its centripetal acceleration is:
Not quite — the answer is D.
v = ωr = 4×5 = 20 m/s; a_c = v²/r = 400/5 = 80 m/s². Equivalently a_c = ω²r = 16×5 = 80 m/s². Option A uses a_c = ωr (missing the square). Option C uses a_c = ω²r² (extra r factor).
Q19Multiplication of Vectors (Dot Product)
Vectors A = 6i + 8j and B = 4i + 3j. The value of A·B is:
Not quite — the answer is B.
A·B = (6 times 4) + (8 times 3) = 24 + 24 = 48. Option C (50) comes from computing magnitudes: |A| = 10, |B| = 5, then multiplying 10 times 5, ignoring the angle between them.
Q20Multiplication of Vectors (Dot Product)
If the dot product of two non-zero vectors is zero, the vectors must be:
Not quite — the answer is C.
A·B = AB cosθ = 0 for non-zero vectors implies cosθ = 0, so θ = 90 degrees. Option A (parallel) gives maximum dot product AB, not zero.
Q21Multiplication of Vectors (Dot Product)
Two vectors each of magnitude 10 units have a dot product of 50. The angle between them is:
Not quite — the answer is B.
A·B = AB cosθ gives 50 = 100 cosθ, so cosθ = 0.5, θ = 60 degrees. Option C (90 degrees) gives dot product = 0, not 50. Option D gives a negative dot product.
Q22Position and Displacement Vectors
The position vector of a particle is defined as the vector drawn from:
Not quite — the answer is A.
A position vector always originates at the chosen reference origin and terminates at the particle. Option B reverses the direction, which would give the negative of the position vector.
Q23Position and Displacement Vectors
A particle moves from point (2, 3) m to point (7, 8) m. The displacement vector is:
Not quite — the answer is B.
Displacement = r₂ − r₁ = (7−2)î + (8−3)ĵ = 5î + 5ĵ m. Option A adds instead of subtracting coordinates. Option C reverses the subtraction order, a common sign-flip error.
Q24Position and Displacement Vectors
Which statement correctly distinguishes position vector from displacement vector?
Not quite — the answer is C.
Shifting the origin changes every position vector but leaves displacement unchanged since the shift cancels in r₂ − r₁. Students confuse the two by assuming both are measured from the origin.
ELITE question · AIR under 50 level
This chapter has 109 ELITE questions for students aiming at the very top. They are only in the app.
Unlock ELITE questions in the appKey Formulas
Quick revision: most questions in this chapter test these facts.
| Concept | Key Formula |
|---|---|
| Projectile — time of flight | T = 2u sinθ / g |
| Projectile — max height | H = u² sin²θ / 2g |
| Projectile — range | R = u² sin2θ / g; max at θ = 45° |
| Centripetal acceleration | a = v²/r = ω²r; directed towards centre |
| Vector addition | |R| = √(A² + B² + 2AB cosθ); tan α = B sinθ / (A + B cosθ) |
| Complementary angles | Same range for θ and (90°−θ) |
What the app covers in this chapter
313 questions in total, each with a detailed explanation.
| Grand Test | 58 |
| Scalars and Vectors | 40 |
| Vector Algebra (Addition, Subtraction, Resolution) | 40 |
| Projectile Motion | 40 |
| Mixed Revision | 40 |
| Uniform Circular Motion | 38 |
| Multiplication of Vectors (Dot Product) | 37 |
| Position and Displacement Vectors | 20 |
Questions students ask
Is Motion in a Plane important for NEET?
Yes — projectile motion formulas and circular motion concepts are tested every year. Numerical problems on range, height and time of flight are common.
Which topics should I revise first?
Master projectile motion formulas (T, H, R), the complementary angle property, vector addition and resolution, and centripetal acceleration in uniform circular motion.
How many questions from this chapter are on RankUp?
The RankUp app has 313 questions on Motion in a Plane, including 109 ELITE questions. Every question has a detailed explanation.
