A particle is in uniform circular motion. Which pair of quantities stays constant throughout the motion?

Its speed and its kinetic energy

Its velocity and its linear momentum

Its velocity and its acceleration

Motion in a Plane

19 NEET-UG practice questions on Motion in a Plane, part of Physics. The first 19 are below; the first 5 with answers and explanations (tap Show answer after you have chosen), the rest in Learn with a free account.

Question 1 · Medium
A river 1 km wide flows at 3 km/h. A swimmer who moves at 5 km/h in still water heads so as to reach the point directly opposite. How long does the crossing take?
1. A12 min
2. B7.5 min
3. C15 min
4. D20 min
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Answer: C · 15 min
To go straight across, the upstream component of the swimmer's velocity must cancel the flow, so the cross-river speed = √(5² − 3²) = 4 km/h. Time = 1/4 h = 15 min.
- A: This is the shortest-time crossing, heading straight across at 5 km/h.
- B: This adds the two speeds as if they were along one line.
- D: This uses the river speed as the crossing speed.
Remember this
For the shortest path, resultant speed = √(v² − u²); for the shortest time, head straight across at speed v.
Question 2 · Easy
A particle is in uniform circular motion. Which pair of quantities stays constant throughout the motion?
1. AIts speed and its kinetic energy
2. BIts velocity and its linear momentum
3. CIts velocity and its acceleration
4. DIts speed and its acceleration
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Answer: A · Its speed and its kinetic energy
In uniform circular motion only the magnitude of velocity is fixed, so speed and kinetic energy stay constant. The directions of velocity, momentum and acceleration change continuously.
- B: Velocity and momentum both change direction continuously.
- C: Both vectors change direction all the time.
- D: Acceleration keeps a fixed magnitude but its direction turns towards the centre.
Remember this
A vector is constant only if both its magnitude and direction stay fixed.
Question 3 · Medium
A football kicked from level ground stays in the air for 4 s. Ignoring air resistance and taking g = 10 m/s², what maximum height does it reach?
1. A10 m
2. B80 m
3. C40 m
4. D20 m
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Answer: D · 20 m
The upward part takes T/2 = 2 s, so the vertical velocity component is 10 × 2 = 20 m/s. H = (20)²/(2 × 10) = 20 m. Check: the fall from the top takes 2 s, and (1/2)(10)(2)² = 20 m. The angle is not needed.
- A: This uses gT²/16, halving the correct result.
- B: This uses (1/2)gT² with the full flight time.
- C: This uses gT²/4 instead of gT²/8.
Remember this
H = gT²/8, whatever the speed and angle of projection.
Question 4 · Hard
A boat leaves point A on one bank with the heading and speeds shown, C being directly opposite A. How far downstream of C does it land? Take sin 37° = 3/5 and cos 37° = 4/5.
Figure: MedExams
1. A300 m
2. B80 m
3. C120 m
4. D480 m
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Answer: C · 120 m
Across the river the boat moves at 5 cos 37° = 4 m/s, so t = 240/4 = 60 s. Along the river its speed is 5 − 5 sin 37° = 5 − 3 = 2 m/s, so drift = 2 × 60 = 120 m. As a check, water carries it 300 m and its heading takes it back 180 m.
- A: Includes the river's drift but ignores the boat's upstream component.
- B: Swaps sine and cosine when resolving the boat's velocity.
- D: Adds the heading component to the river speed, as if heading downstream.
Remember this
Crossing time depends only on the across component; drift uses the net component along the river.
Question 5 · Medium
A ball is thrown from level ground at an acute angle above the horizontal with speed u, and lands at the same level after time T. Ignoring air resistance, which graph shows its speed against time?
Figure: MedExams
1. AGraph A
2. BGraph B
3. CGraph D
4. DGraph C
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Answer: A · Graph A
The horizontal velocity stays constant and the vertical velocity changes uniformly with time, so speed falls smoothly to the non-zero horizontal component at T/2 and rises back to u at T. Graph A shows this rounded dip.
- B: Graph B has zero speed at the top, which fits only a throw straight up.
- C: Graph D has speed rising on the way up, though gravity slows the ascent.
- D: Graph C keeps speed constant, ignoring gravity's change of the vertical velocity.
Remember this
At the top of a projectile path only the vertical velocity is zero; the speed equals the horizontal component.
Question 6 · Easy
On a grid of 1 m squares, two displacement vectors A and B start from the same point. What is the magnitude of A + B?
Figure: MedExams
1. A5 m
2. B7 m
3. C√5 m
4. D4 m
Answer and explanation in LearnFree account
Question 7 · Medium
During a spin test, a wheel of radius 0.5 m turns uniformly at 120 revolutions per minute. Taking π² = 10, what is the centripetal acceleration of a point on its rim?
1. A80 m/s²
2. B320 m/s²
3. C2 m/s²
4. D160 m/s²
Answer and explanation in LearnFree account
Question 8 · Easy
Ignoring air resistance, what is the angle between the velocity and the acceleration of a projectile at the highest point of its path?
1. A45°
2. B90°
3. C0°
4. D180°
Answer and explanation in LearnFree account
Question 9 · Hard
When a man walks east at 4 m/s, the rain appears to him to fall vertically. When he speeds up to 8 m/s, the rain appears to fall at 30° to the vertical. What is the actual velocity of the rain?
1. A8 m/s, at 30° to the vertical, slanting towards the east
2. B8 m/s, at 30° to the vertical, slanting towards the west
3. C4√3 m/s, vertically downward
4. D8 m/s, at 60° to the vertical, slanting towards the east
Answer and explanation in LearnFree account
Question 10 · Medium
With the same speed of projection from level ground and no air resistance, which pair of angles of projection gives equal horizontal ranges?
1. A40° and 80°
2. B25° and 65°
3. C30° and 45°
4. D25° and 50°
Answer and explanation in LearnFree account
Question 11 · Easy
A ball is projected obliquely from level ground. Ignoring air resistance, which quantity stays constant throughout its flight?
1. AThe direction of its velocity
2. BThe horizontal component of its velocity
3. CIts speed
4. DThe vertical component of its velocity
Answer and explanation in LearnFree account
Question 12 · Hard
A particle moves on a circle of radius 2 m at a constant speed of 4 m/s. What is the magnitude of its average acceleration while it covers half a revolution?
1. A8 m/s²
2. BZero
3. C16/π m/s²
4. D8/π m/s²
Answer and explanation in LearnFree account
Question 13 · Medium
Car A moves due east at 30 m/s and car B moves due north at 40 m/s. What is the velocity of B as seen by a passenger in A? (Take tan 53° = 4/3.)
1. A50 m/s, at 53° north of west
2. B10 m/s, due north
3. C70 m/s, towards the north-east
4. D50 m/s, at 53° north of east
Answer and explanation in LearnFree account
Question 14 · Medium
A stone is thrown horizontally at 40 m/s from the top of a cliff 45 m high. Taking g = 10 m/s² and ignoring air resistance, with what speed does it strike the ground below?
1. A40 m/s
2. B50 m/s
3. C30 m/s
4. D70 m/s
Answer and explanation in LearnFree account
Question 15 · Medium
Two forces of equal magnitude F act at a point, and their resultant also has magnitude F. What is the angle between the two forces?
1. A90°
2. B60°
3. C180°
4. D120°
Answer and explanation in LearnFree account
Question 16 · Medium
A ball is projected from level ground. At the highest point of its path its speed is half its speed of projection. Ignoring air resistance, at what angle to the horizontal was it projected?
1. A60°
2. B30°
3. C45°
4. D75°
Answer and explanation in LearnFree account
Question 17 · Easy
Three vectors P, Q and R are drawn head to tail in the figure, so that they form a closed triangle. Which relation between them is correct?
Figure: MedExams
1. AP + Q + R = 0
2. BP + R = Q
3. CQ + R = P
4. DP + Q = R
Answer and explanation in LearnFree account
Question 18 · Hard
A ball is thrown from the ground at 20 m/s, at 45° above the horizontal, towards a vertical wall 30 m away, as shown. Taking g = 10 m/s² and ignoring air resistance, at what height does it strike the wall, and is it then rising or falling?
Figure: MedExams
1. A22.5 m, while falling
2. B7.5 m, while rising
3. C7.5 m, while falling
4. D18.75 m, while rising
Answer and explanation in LearnFree account
Question 19 · Medium
The figure plots the height of a stone against its horizontal distance from O, its launch point on level ground. Taking g = 10 m/s² and ignoring air resistance, find its launch speed.
Figure: MedExams
1. A20 m/s
2. B20√2 m/s
3. C40 m/s
4. D20√5 m/s
Answer and explanation in LearnFree account

Motion in a Plane

A river 1 km wide flows at 3 km/h. A swimmer who moves at 5 km/h in still water heads so as to reach the point directly opposite. How long does the crossing take?

A particle is in uniform circular motion. Which pair of quantities stays constant throughout the motion?

A football kicked from level ground stays in the air for 4 s. Ignoring air resistance and taking g = 10 m/s², what maximum height does it reach?

A boat leaves point A on one bank with the heading and speeds shown, C being directly opposite A. How far downstream of C does it land? Take sin 37° = 3/5 and cos 37° = 4/5.

A ball is thrown from level ground at an acute angle above the horizontal with speed u, and lands at the same level after time T. Ignoring air resistance, which graph shows its speed against time?

On a grid of 1 m squares, two displacement vectors A and B start from the same point. What is the magnitude of A + B?

During a spin test, a wheel of radius 0.5 m turns uniformly at 120 revolutions per minute. Taking π² = 10, what is the centripetal acceleration of a point on its rim?

Ignoring air resistance, what is the angle between the velocity and the acceleration of a projectile at the highest point of its path?

When a man walks east at 4 m/s, the rain appears to him to fall vertically. When he speeds up to 8 m/s, the rain appears to fall at 30° to the vertical. What is the actual velocity of the rain?

With the same speed of projection from level ground and no air resistance, which pair of angles of projection gives equal horizontal ranges?

A ball is projected obliquely from level ground. Ignoring air resistance, which quantity stays constant throughout its flight?

A particle moves on a circle of radius 2 m at a constant speed of 4 m/s. What is the magnitude of its average acceleration while it covers half a revolution?

Car A moves due east at 30 m/s and car B moves due north at 40 m/s. What is the velocity of B as seen by a passenger in A? (Take tan 53° = 4/3.)

A stone is thrown horizontally at 40 m/s from the top of a cliff 45 m high. Taking g = 10 m/s² and ignoring air resistance, with what speed does it strike the ground below?

Two forces of equal magnitude F act at a point, and their resultant also has magnitude F. What is the angle between the two forces?

A ball is projected from level ground. At the highest point of its path its speed is half its speed of projection. Ignoring air resistance, at what angle to the horizontal was it projected?

Three vectors P, Q and R are drawn head to tail in the figure, so that they form a closed triangle. Which relation between them is correct?

A ball is thrown from the ground at 20 m/s, at 45° above the horizontal, towards a vertical wall 30 m away, as shown. Taking g = 10 m/s² and ignoring air resistance, at what height does it strike the wall, and is it then rising or falling?

The figure plots the height of a stone against its horizontal distance from O, its launch point on level ground. Taking g = 10 m/s² and ignoring air resistance, find its launch speed.