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JEE • PHYSICS • MOTION IN PLANE

Motion in plane practice · Medium

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These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Showing 1-30 of 388 questions
1 Medium
1 of 388
Analyzing +4 | -1
Given, P⃗=A⃗+B⃗  and P=A+B.\mathrm{\vec P} = \mathrm{\vec A} + \mathrm{\vec B}\,\,\mathrm{and}\,P = A + B. The angle between A⃗ and B⃗\mathrm{\vec A}\,and\,\mathrm{\vec B} is
View answer and explanation
Correct option: A
00{0^0}
Option A (00{0^0}) is correct because the magnitude of the resultant vector is the sum of the magnitudes of the individual vectors, implying they are in the same direction.
2 Medium
2 of 388
Analyzing +4 | -1
Assertion: The necessary condition for motion in two dimensions, velocity and acceleration vectors should have any angle between 0∘0^{\circ} and 90∘90^{\circ} between them.
Reason: For two-dimensional or three-dimensional motion, velocity and acceleration of an object works in opposite direction.
View answer and explanation
Correct option: D
If both assertion and reason are false
The correct answer is C because the assertion is correct (angular momentum is conserved), but the reason is incorrect (linear momentum conservation doesn't necessarily lead to angular momentum conservation).
3 Medium
3 of 388
Understanding +4 | -1
At the top of the trajectory of a projectile, the direction of its velocity and acceleration are
View answer and explanation
Correct option: A
perpendicular to each other
Option A is correct because at the top of the trajectory, the velocity is horizontal and the acceleration due to gravity is vertical, making them perpendicular.
4 Medium
4 of 388
Application +4 | -1
A ball is thrown at an angle θ\theta and another ball is thrown at an angle (90∘−θ)\left(90^{\circ}-\theta\right) with the horizontal direction from the same point with velocity 39.2 ms−139.2 \mathrm{~ms}^{-1}. The second ball reaches 50 m50 \mathrm{~m} higher than the first ball. Find their individual heights. Take g=9.8 ms−2{g}=9.8 \mathrm{~ms}^{-2}.
View answer and explanation
Correct option: A
14.2 m,64.2 m14.2 \mathrm{~m}, 64.2 \mathrm{~m}
Option A (14.2 m,64.2 m14.2 \mathrm{~m}, 64.2 \mathrm{~m}) is correct because the individual heights are calculated using projectile motion equations and the given condition that the second ball reaches 50m higher than the first.
5 Medium
5 of 388
Analyzing +4 | -1
Assertion: The drover in a vehicle moving with a constant speed on a straight road is in a non-inertial frame of reference.

Reason: A reference frame in which Newton's laws of motion are applicable is non-inertial.
View answer and explanation
Correct option: C
If assertion is true, but reason is false.
Option C is correct. A driver in a vehicle moving at constant speed is in an inertial frame, and Newton's laws are applicable in inertial frames.
6 Medium
6 of 388
Understanding +4 | -1
When a projectile is fired at an angle θ\theta with respect to horizontal with velocity uu, the horizontal component, ignoring air resistance
View answer and explanation
Correct option: A
remains same.
The correct answer is A (remains same) because in projectile motion, the horizontal component of velocity remains constant in the absence of air resistance.
7 Medium
7 of 388
Analyzing +4 | -1
Statement-I: If the magnitude of the sum of two unit vectors is a unit vector, then magnitude of their difference is 3\sqrt{3}
Statement-II: ∣a⃗∣+∣b⃗∣=∣a⃗+b⃗∣|\vec{a}|+|\vec{b}|=|\vec{a}+\vec{b}|
View answer and explanation
Correct option: B
Statement-I is true and statement-II is false
Option B (Statement-I is true and statement-II is false) is correct because the magnitude of the difference of two unit vectors forming an angle of 120 degrees is sqrt(3), and the triangle inequality doesn't always hold.
8 Medium
8 of 388
Analyzing +4 | -1
When air resistance is taken into account while dealing with the motion of the projectile which of the following properties of the projectile, shows an increase?
View answer and explanation
Correct option: D
The angle at which the projectile strikes the ground
Option D (The angle at which the projectile strikes the ground) is correct because air resistance reduces horizontal velocity more than vertical, increasing the impact angle.
9 Medium
9 of 388
Understanding +4 | -1
A→ . B→=−∣A∣∣B∣\overrightarrow A \,.\,\overrightarrow B = - \left| A \right|\left| B \right|, then
View answer and explanation
Correct option: C
A→ and B→\overrightarrow A \,and\,\overrightarrow B act in the opposite direction
Option C (A→ and B→\overrightarrow A \,and\,\overrightarrow B act in the opposite direction) is correct because the dot product is negative when the angle between the vectors is 180 degrees.
10 Medium
10 of 388
Analyzing +4 | -1
Assertion: In projectile motion, when horizontal range is n{n} times the maximum height, the angle of projection is given by tan⁡θ=4n\tan \theta=\frac{4}{n}
Reason: In the case of horizontal projection the magnitude of vertical velocity increases with time.
View answer and explanation
Correct option: B
If both Assertion & reason are True but Reason is not a correct explanation of the Assertion
Option B (If both Assertion & reason are True but Reason is not a correct explanation of the Assertion) is correct because both the formula relating range, height, and angle, and the statement about vertical velocity in horizontal projection are true, but unrelated.
11 Medium
11 of 388
Understanding +4 | -1
The angle between A→+B→andA→×B→\overrightarrow A + \overrightarrow B \mathrm{ and }\overrightarrow A \times \overrightarrow B is
View answer and explanation
Correct option: A
0
Option A (0) is correct because the dot product of any vector with a cross product involving that vector is always zero.
12 Medium
12 of 388
Remembering +4 | -1
For angle …X…\ldots X \ldots the projectile has maximum range and it is equal to ...X.... Here, X\mathrm{X} and Y\mathrm{Y} refer to
View answer and explanation
Correct option: C
π4\frac{\pi}{4} and v02g\frac{v_0^2}{g}
Option C (π4\frac{\pi}{4} and v02g\frac{v_0^2}{g}) is correct because the maximum range of a projectile is achieved at an angle of 45 degrees (π4\frac{\pi}{4} radians) and is equal to v02g\frac{v_0^2}{g}.
13 Medium
13 of 388
Analyzing +4 | -1
Identical guns fire identical bullets horizontally at the same speed from the same height above level planes, one on the Earth and another one on the Moon. Which of the following statement are "TRUE"?

I) The horizontal distance travelled by the bullet is greater for the moon.

II) The flight time is less for the bullet on the Earth.

III) The velocities of the bullets at impact are the same.
View answer and explanation
Correct option: C
I and II only
Option C (I and II only) is correct because the horizontal distance is greater on the Moon due to lower gravity, and the flight time is less on Earth due to higher gravity.
14 Medium
14 of 388
Application +4 | -1
If ∣A⃗×B⃗∣=3A⃗⋅B⃗|\vec{A} \times \vec{B}|=\sqrt{3} \vec{A} \cdot \vec{B} then the value of ∣A⃗+B⃗∣|\vec{A}+\vec{B}| is
View answer and explanation
Correct option: A
(A2+B2+AB)1/2\left(A^2+B^2+A B\right)^{1 / 2}
Option A ((A2+B2+AB)1/2\left(A^2+B^2+A B\right)^{1 / 2}) is correct because it correctly uses the given relationship between the cross product and dot product to find the angle between the vectors and then calculates the magnitude of the sum.
15 Medium
15 of 388
Application +4 | -1
If A⃗=4i^+nj^−2k^\vec{A}=4 \hat{i}+n \hat{j}-2 \hat{k} and B⃗=2i^+3j^+k^\vec{B}=2 \hat{i}+3 \hat{j}+\hat{k}, then find the value of nn so that A⃗⊥B⃗\vec{A} \perp \vec{B}.
View answer and explanation
Correct option: C
n=−2n=-2
Option C (n=−2n=-2) is correct because the dot product of two perpendicular vectors is zero, and solving the dot product equation yields n = -2.

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16 Medium
16 of 388
Analyzing +4 | -1
A swimmer crosses a flowing stream of width ω\omega to and fro in time t1.t_1. The time taken to cover the same distance up and down the stream is t2.t_2. If t3t_3 is the time the swimmer would take to swim a distance 2ω2 \omega in still water, then
View answer and explanation
Correct option: A
t12=t2t3t_1^2=t_2 t_3
Option A (t12=t2t3t_1^2=t_2 t_3) is correct because it is derived from the relationships between the times taken to cross the stream and swim in still water, considering the swimmer's speed and the stream's velocity.
17 Medium
17 of 388
Analyzing +4 | -1
If an object is thrown at an angle of 60∘60^{\circ} with horizontal, find elevation angle of the object at its highest point as seen from the point of projection
View answer and explanation
Correct option: A
tan⁡−132\tan ^{-1} \frac{\sqrt{3}}{2}
Option A (tan⁡−132\tan ^{-1} \frac{\sqrt{3}}{2}) is correct because it is derived from the relationship between the maximum height and half the range of a projectile at its highest point.
18 Medium
18 of 388
Analyzing +4 | -1
Two projectile are thrown from the ground at different angles so that their initial vertical component of velocities are equal, then they have same
View answer and explanation
Correct option: D
Both (2) and (3)
Option D is correct. Time of flight and maximum height depend only on the initial vertical component of velocity, which is the same for both projectiles.
19 Medium
19 of 388
Understanding +4 | -1
Assertion: Current and time both have direction as well
as magnitude but still are not considered vector.

Reason: They do not follow laws of vector addition.
View answer and explanation
Correct option: A
If both assertion and reason are true and reason is the
correct explanation of the assertion.
Option A (If both assertion and reason are true and reason is the correct explanation of the assertion.) is correct because current and time are scalar quantities as they do not obey the laws of vector addition.
20 Medium
20 of 388
Understanding +4 | -1
Assertion: Any two vectors can be added.
Reason: The vectors are added by applying the laws of algebra.
View answer and explanation
Correct option: D
If both assertion and reason are false.
Option D (If both assertion and reason are false) is correct because vectors can only be added if they represent the same physical quantity, and they are added using vector algebra, not standard algebra.
21 Medium
21 of 388
Analyzing +4 | -1
Assertion : A body is thrown with a velocity u inclined to the horizontal at some angle. It moves along a parabolic path and falls to the ground. Linear momentum of the body, during its motion, will remain conserve.
Reason : Throughout the motion of the body, a constant force acts on it.
View answer and explanation
Correct option: D
Assertion is incorrect, reason is correct.
The correct answer is D (Assertion is incorrect, reason is correct) because linear momentum is not conserved in projectile motion due to gravity, and a constant gravitational force does act on the body.
22 Medium
22 of 388
Understanding +4 | -1
Assertion : The horizontal range is same when the angle of projection is greater than 45∘45^{\circ} by certain value and less than 45∘45^{\circ} by the same value.
Reason: If θ=45∘+α\theta=45^{\circ}+\alpha, then

R1=u2sin⁡2(45∘+α)g=u2cos⁡2αg\mathrm{R}_1=\frac{\mathrm{u}^2 \sin 2\left(45^{\circ}+\alpha\right)}{\mathrm{g}}=\frac{\mathrm{u}^2 \cos 2 \alpha}{\mathrm{g}}

If θ=45∘−α\theta=45^{\circ}-\alpha, then R2=u2sin⁡2(45∘−α)g=u2cos⁡2αg\mathrm{R}_2=\frac{\mathrm{u}^2 \sin 2\left(45^{\circ}-\alpha\right)}{\mathrm{g}}=\frac{\mathrm{u}^2 \cos 2 \alpha}{\mathrm{g}}
View answer and explanation
Correct option: A
Assertion is correct, reason is correct; reason is a correct explanation for assertion.
Option A (Assertion is correct, reason is correct; reason is a correct explanation for assertion) is correct because the horizontal range is the same for angles equidistant from 45 degrees, and the reason provides the correct mathematical justification.
23 Medium
23 of 388
Application +4 | -1
The horizontal and vertical displacement x and y of a projectile at a given time t are given by x=6t metre and y=8t−5t2y = 8t - 5{t^2} metre. The range of the projectile in metre is
View answer and explanation
Correct option: A
9.6
Option A (9.6) is correct because the range of the projectile is calculated from the given equations of motion, resulting in 9.6 meters.
24 Medium
24 of 388
Understanding +4 | -1
Assertion: The time taken by a boat to cover a certain distance upstream is more than the time taken to cover the same distance downstream.

Reason: The speed of the boat is lesser while moving upstream as compared to downstream due to the speed of the stream.
View answer and explanation
Correct option: A
Both Assertion and Reason are true, and Reason is the correct explanation for Assertion
Option A (Both the Assertion and Reason are true, and Reason is the correct explanation for Assertion) is correct because the boat's speed is reduced upstream due to the stream's opposing force, increasing the time taken to cover the distance.
25 Medium
25 of 388
Understanding +4 | -1
Two particles are projected with same speed but at angles of projection (450−θ) and (450+θ)\left( {{{45}^0} - \theta } \right)\,and\,\left( {{{45}^0} + \theta } \right) Then their horizontal ranges are in the ratio of
View answer and explanation
Correct option: C
1:11:1
Option C (1:1) is correct because the ranges are the same for complementary angles of projection relative to 45 degrees.
26 Medium
26 of 388
Understanding +4 | -1
If a⃗+b⃗=c⃗\vec{a}+\vec{b}=\vec{c} and a+b=ca+b=c, then the angle included between a⃗\vec{a} and b⃗\vec{b} is
View answer and explanation
Correct option: D
zero
Option D (zero) is correct because if the magnitude of the resultant vector is equal to the sum of the magnitudes of the individual vectors, the vectors must be parallel, implying an angle of 0 degrees between them.
27 Medium
27 of 388
Analyzing +4 | -1
Assertion: The magnitude R=A2+B2R=\sqrt{A^2+B^2} of the resultant of two vectors AA and BB is less than the magnitude of either vector.
Reason: The resultant of two vectors is calculated by using the law of parallelogram of vectors.
View answer and explanation
Correct option: B
If both assertion and reason are true but reason is not the correct explanation of assertion
Option B (If both assertion and reason are true but reason is not the correct explanation of assertion) is correct because the resultant magnitude can be less than either vector if the angle between them is greater than 90 degrees, and the law of parallelogram is used to calculate the resultant, but the latter doesn't explain the former.
28 Medium
28 of 388
Analyzing +4 | -1
In a tetrahedron OABCO A B C, the edges are of lengths, ∣OA∣=∣BC∣=a,∣OB∣=∣AC∣=b,∣OC∣=∣AB∣=c|O A|=|B C|=a,|O B|=|A C|=b,|O C|=|A B|=c. Let G1G_1 and C2C_2 be the centroids of the triangle ABCA B C and AOCA O C such that OG1⊥BG2O G_1 \perp B G_2, then the value of a2+c2b2\frac{a^2+c^2}{b^2} is
View answer and explanation
Correct option: B
3
Option B (3) is correct because by using the given condition OG1⋅BG2=0OG_1 \cdot BG_2 = 0 and the properties of centroids, we can derive the relationship a2+c2b2=3\frac{{a^2 + c^2}}{{b^2}} = 3.
29 Medium
29 of 388
Understanding +4 | -1
Assertion: In a projectile motion, the vertical velocity of the particle is continuously decreased during its ascending motion.
Reason: In projectile motion downward constant acceleration is present in vertical direction.
View answer and explanation
Correct option: A
If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion
Option A (If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion) is correct because the vertical velocity decreases due to the constant downward acceleration due to gravity.
30 Medium
30 of 388
Application +4 | -1
A bullet is fired horizontally with a velocity of 80  ms−180\mathrm{\;m}{\mathrm{s}^{ - 1}}. During the first second,
View answer and explanation
Correct option: D
It falls 4.9 m
Option D (It falls 4.9 m) is correct because it is calculated using the equation of motion for vertical displacement under gravity.
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