Motion in a Plane · Physics · NEET
MCQ (Single Correct Answer)
1
A bob is whirled in a horizontal circle by means of a string at an initial speed of $$10 \mathrm{~rpm}$$. If the tension in the string is quadrupled while keeping the radius constant, the new speed is:
NEET 2024 (Re-Examination)
2
Let $$\omega_1, \omega_2$$ and $$\omega_3$$ be the angular speed of the second hand, minute hand and hour hand of a smoothly running analog clock, respectively. If $$x_1, x_2$$ and $$x_3$$ are their respective angular distances in 1 minute then the factor which remains constant $$(k)$$ is
NEET 2024 (Re-Examination)
3
A ball is projected from point A with velocity $$20 \mathrm{~m} \mathrm{~s}^{-1}$$ at an angle $$60^{\circ}$$ to the horizontal direction. At the highest point $$\mathrm{B}$$ of the path (as shown in figure), the velocity $$\mathrm{v} \mathrm{m} \mathrm{s}^{-1}$$ of the ball will be:
NEET 2023 Manipur
4
A particle is executing uniform circular motion with velocity $$\vec{v}$$ and acceleration $$\vec{a}$$. Which of the following is true?
NEET 2023 Manipur
5
A bullet is fired from a gun at the speed of $$280 \mathrm{~ms}^{-1}$$ in the direction $$30^{\circ}$$ above the horizontal. The maximum height attained by the bullet is
$$\left(g=9.8 \mathrm{~ms}^{-2}, \sin 30^{\circ}=0.5\right)$$:-
NEET 2023
6
A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity $$4 \mathrm{~m} \mathrm{~s}^{-1}$$. The ball strikes the water surface after $$4 \mathrm{~s}$$. The height of bridge above water surface is (Take $$g=10 \mathrm{~m} \mathrm{~s}^{-2}$$ )
NEET 2023
7
A cricket ball is thrown by a player at a speed of 20 m/s in a direction 30$$^\circ$$ above the horizontal. The maximum height attained by the ball during its motion is
(g = 10 m/s2)
NEET 2022 Phase 2
8
A ball is projected with a velocity, 10 ms$$-$$1, at an angle of 60$$^\circ$$ with the vertical direction. Its speed at the highest point of its trajectory will be
NEET 2022 Phase 1
9
A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution.
If this particle were projected with the same speed at an angle '$$\theta$$' to the horizontal, the maximum height attained by it equals 4R. The angle of projection, $$\theta$$, is then given by :
If this particle were projected with the same speed at an angle '$$\theta$$' to the horizontal, the maximum height attained by it equals 4R. The angle of projection, $$\theta$$, is then given by :
NEET 2021
10
A car starts from rest and accelerates at 5m/s2. At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t = 6 s? (Take g = 10 m/s2)
NEET 2021
11
When an object is shot from the bottom of a long smooth inclined plane kept at an angle 60o with horizontal, it can travel a distance x1 along the plane. But when the inclination is decreased to 30o and the same object is shot with the same velocity, it can travel x2 distance. Then x1 : x2 will be :
NEET 2019
12
A particle moving with velocity
$$\overrightarrow V $$ is acted by three forces shown by the vector triangle PQR. The velocity of the particle will :
NEET 2019
13
The x and y coordinates of the particle at any time are x = 5t $$-$$ 2t2 and y = 10t respectively, where x and y are in metres and t in seconds. The acceleration of the particle at t = 2 s is
NEET 2017
14
In the given figure, a = 15 m s$$-$$2 represents the total acceleration of particle moving in the clockwise direction in a circle of radius R = 2.5 m at a given instant of time. The speed of the particle is
NEET 2016 Phase 2
15
If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is
NEET 2016 Phase 1
16
A particle moves so that its position vector is given by $$\overrightarrow r = \cos \omega t\,\widehat x + \sin \,\omega t\,\widehat y,$$ where $$\omega $$ is a constant.
Which of the following is true?
Which of the following is true?
NEET 2016 Phase 1
17
The positions vector of a particle $$\overrightarrow R $$ as a function of time is given by $$\overrightarrow R $$ = 4sin(2$$\pi $$t)$$\widehat i$$ + 4cos(2$$\pi $$t)$$\widehat j$$. Where R is in meters, t is in seconds and $$\widehat i$$ and $$\widehat j$$ denote unit vectors along x-and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?
AIPMT 2015
18
If vectors $$\overrightarrow A = \cos \omega t\widehat i + \sin \omega t\widehat j$$ and $$\overrightarrow B = \cos {{\omega t} \over 2}\widehat i + \sin {{\omega t} \over 2}\widehat j$$ are functions of time, then the value of t at which they are orthogonal to each other is
AIPMT 2015
19
A ship A is moving Westwards with a speed of 10 km h$$-$$1 and a ship B 100 km South of A, is moving Northwards with a speed of 10 km h$$-$$1. The time after which the distance between them becomes shortest, is
AIPMT 2015 Cancelled Paper
20
A particle is moving such that is position coordinates (x, y) are (2 m, 3 m) at time t = 0, (6 m, 7 m)
at time t = 2 s and (13 m, 14 m) at time t = 5 s.
Average velocity vector $$\left( {{{\overrightarrow v }_{av}}} \right)$$ from t = 0 to t = 5 s is
at time t = 2 s and (13 m, 14 m) at time t = 5 s.
Average velocity vector $$\left( {{{\overrightarrow v }_{av}}} \right)$$ from t = 0 to t = 5 s is
AIPMT 2014
21
A projectile is fired from the surface of the earth with a velocity of 5 m s$$-$$1 and angle $$\theta $$
with the horizontal. Another projectile fired from another planet with a velocity of 3 m s$$-$$1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in m s$$-$$2) is
(Given g = 9.8 m s$$-$$2)
(Given g = 9.8 m s$$-$$2)
AIPMT 2014
22
Vectors $$\overrightarrow A ,\overrightarrow B $$ and $$\overrightarrow C $$ are such that $$\overrightarrow A .\overrightarrow B = 0$$ and $$\overrightarrow A .\overrightarrow C = 0$$. Then the vector parallel to $$\overrightarrow A $$ is
NEET 2013 (Karnataka)
23
The velocity of a projectile at the initial point A is $$\left( {2\widehat i + 3\widehat j} \right)$$ m/s. It's velocity (in m/s) at point B is
NEET 2013
24
A particle has initial velocity $$\left( {2\overrightarrow i + 3\overrightarrow j } \right)$$ and acceleration $$\left( {0.3\overrightarrow i + 0.2\overrightarrow j } \right)$$. The magnitude of velocity after 10 seconds will be
AIPMT 2012 Prelims
25
The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is
AIPMT 2012 Prelims
26
A projectile is fired at an angle of 45o with the horizontal. Elevation angle of the projectile at its highest point as seen from the point of projection, is
AIPMT 2011 Mains
27
A body is moving with velocity 30 m/s towards east . After 10 seconds its velocity becomes 40 m/s towards north. The average acceleration of the body is
AIPMT 2011 Prelims
28
A missile is fired for maximum range with an initial velocity of 20 m/s. If g = 10 m/s2, the range of the missile is
AIPMT 2011 Prelims
29
A particle moves in a circle of radius 5 cm with constant speed and time period 0.2$$\pi $$ s. The acceleration of the particle is
AIPMT 2011 Prelims
30
The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is
AIPMT 2010 Mains
31
A particle moves in x-y plane according to rule x = asin$$\omega $$t and y = acos$$\omega $$t. The particle follows
AIPMT 2010 Mains
32
Six vectors, $$\overrightarrow a $$ through $$\overrightarrow f $$ have the magnitudes and directions indicated in the figure. Which of the following statements is true ?
AIPMT 2010 Prelims
33
A particle has initial velocity $$\left( {3\widehat i + 4\widehat j} \right)$$ and has acceleration $$\left( {0.4\widehat j + 0.3\widehat j} \right).$$ Its speed after 10 s is
AIPMT 2010 Prelims
34
A particle shows distance - time curve as given in this figure. The maximum instaneous velocity of the particle is around the point
AIPMT 2008
35
$$\overrightarrow A $$ and $$\overrightarrow B $$ are two vectors and $$\theta $$ is the angle between them, if $$\left| {\overrightarrow A \times \overrightarrow B } \right| = \sqrt 3 \left( {\overrightarrow A .\overrightarrow B } \right),$$ the value of $$\theta $$ is
AIPMT 2007
36
A particle starting from the origin (0, 0) moves in a straight line in the (x, y) planes. Its coordinates at a later time are $$\left( {\sqrt 3 ,3} \right)$$. The path of the particle makes with the x-axes an angle of
AIPMT 2007
37
The vectors $$\overrightarrow A $$ and $$\overrightarrow B $$ are such that $$\left| {\overrightarrow A + \overrightarrow B } \right| = \left| {\overrightarrow A - \overrightarrow B } \right|.$$ The angle between the two vectors is
AIPMT 2006
38
For angles of projection of a projectile at angle (45o $$-$$ $$\theta $$) and (45o + $$\theta $$), the horizontal range described by the projectile are in the ratio of
AIPMT 2006
39
If a vector $$2\widehat i + 3\widehat j + 8\widehat k$$ is perpendicular to the vector $$4\widehat j - 4\widehat i + \alpha \widehat k,$$ then the value of $$\alpha $$ is
AIPMT 2005
40
If the angle between the vectors $$\overrightarrow A $$ and $$\overrightarrow B $$ is $$\theta $$, the value of the product $$\left( {\overrightarrow B \times \overrightarrow A } \right).\overrightarrow A $$ is equal to
AIPMT 2005
41
Two boys are standing at the ends A and B of a ground where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity v1. The boy at A starts running simultaneously with velocity v and catches the other in a time t, where t is
AIPMT 2005
42
If $$\left| {\overrightarrow A \times \overrightarrow B } \right| = \sqrt 3 \overrightarrow A .\overrightarrow B $$ then the value of $$\left| {\overrightarrow A + \overrightarrow B } \right|$$ is
AIPMT 2004
43
The vector sum of two forces is perpendicular to their vector differences. In that case, the forces
AIPMT 2003
44
A particle A is dropped from a height and another particle B is projected in horizontal direction with speed of 5/sec from the same height then correct statement is
AIPMT 2002
45
Two particles having mass M and m are moving in a circular path having radius R and r. If their time period are same then the ratio of angular velocity will be
AIPMT 2001
46
If $$\left| {\overrightarrow A + \overrightarrow B } \right| = \left| {\overrightarrow A } \right| + \left| {\overrightarrow B } \right|$$ then angle between A and B will be
AIPMT 2001
47
A man is slipping on a frictionless inclined plane and a bag falls down from the same height. Then the velocity of both is related as
AIPMT 2000
48
The width of river is 1 km. The velocity of boat is 5 km/hr. The boat covered the width of river in shortest time 15 min. Then the velocity of river stream is
AIPMT 2000
49
Two projectiles of same mass and with same velocity are thrown at an angle 60o and 30o with the horizontal, then which will remain same
AIPMT 2000