Question 1: Palette 1/50

NEET 2024 MCQ

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:

A

20 rpm

B

40 rpm

C

5 rpm

D

10 rpm

Question 2: Palette 2/50

NEET 2024 MCQ

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

A

$\frac{\omega_1}{x_1}=\frac{\omega_2}{x_2}=\frac{\omega_3}{x_3}=k$

B

$\omega_1 x_1=\omega_2 x_2=\omega_3 x_3=k$

C

$\omega_1 x_1^2=\omega_2 x_2^2=\omega_3 x_3^2=k$

D

$\omega_1^2 x_1=\omega_2^2 x_2=\omega_3^2 x_3=k$

Question 3: Palette 3/50

NEET 2023 MCQ

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:

A

20

B

$10 \sqrt{3}$

C

Zero

D

10

Question 4: Palette 4/50

NEET 2023 MCQ

A particle is executing uniform circular motion with velocity $\vec{v}$ and acceleration $\vec{a}$. Which of the following is true?

A

$\vec{v}$ is a constant; $\vec{a}$ is not a constant

B

$\vec{v}$ is not a constant; $\vec{a}$ is not a constant

C

$\vec{v}$ is a constant; $\vec{a}$ is a constant

D

$\vec{v}$ is not a constant; $\vec{a}$ is a constant

Question 5: Palette 5/50

NEET 2023 MCQ

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

$\left(g=9.8 \mathrm{~ms}^{-2}, \sin 30^{\circ}=0.5\right)$:-

A

2000 m

B

1000 m

C

3000 m

D

2800 m

Question 6: Palette 6/50

NEET 2023 MCQ

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 $g=10 \mathrm{~m} \mathrm{~s}^{-2}$ )

A

60 m

B

64 m

C

68 m

D

56 m

Question 7: Palette 7/50

NEET 2022 MCQ

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)

A

25 m

B

5 m

C

10 m

D

20 m

Question 8: Palette 8/50

NEET 2022 MCQ

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

A

Zero

B

5$\sqrt3$ ms^$-$1

C

5 ms^$-$1

D

10 ms^$-$1

Question 9: Palette 9/50

NEET 2021 MCQ

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 :

A

$\theta = {\sin ^{ - 1}}{\left( {{{2g{T^2}} \over {{\pi ^2}R}}} \right)^{1/2}}$

B

$\theta = {\cos ^{ - 1}}{\left( {{{g{T^2}} \over {{\pi ^2}R}}} \right)^{1/2}}$

C

$\theta = {\cos ^{ - 1}}{\left( {{{{\pi ^2}R} \over {g{T^2}}}} \right)^{1/2}}$

D

$\theta = {\sin ^{ - 1}}{\left( {{{{\pi ^2}R} \over {g{T^2}}}} \right)^{1/2}}$

Question 10: Palette 10/50

NEET 2021 MCQ

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)

A

20$\sqrt 2 $ m/s, 10 m/s²

B

20 m/s, 5 m/s²

C

20 m/s, 0

D

20$\sqrt 2 $ m/s, 0

Question 11: Palette 11/50

NEET 2019 MCQ

A particle moving with velocity $\overrightarrow V $ is acted by three forces shown by the vector triangle PQR. The velocity of the particle will :

A

remain constant

B

increase

C

decrease

D

change according to the smallest force $\overrightarrow {QR} $

Question 12: Palette 12/50

NEET 2019 MCQ

When an object is shot from the bottom of a long smooth inclined plane kept at an angle 60^o with horizontal, it can travel a distance x₁ along the plane. But when the inclination is decreased to 30^o and the same object is shot with the same velocity, it can travel x₂ distance. Then x₁ : x₂ will be :

A

1 : $\sqrt 2 $

B

$\sqrt 2 $ : 1

C

1 : $\sqrt 3 $

D

1 : 2$\sqrt 3 $

Question 13: Palette 13/50

NEET 2017 MCQ

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

A

5 m s^$-$2

B

$-$4 m s^$-$2

C

$-$8 m s^$-$2

D

0

Question 14: Palette 14/50

NEET 2016 MCQ

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

A

4.5 m s^$-$1

B

5.0 m s^$-$1

C

5.7 m s^$-$1

D

6.2 m s^$-$1

Question 15: Palette 15/50

NEET 2016 MCQ

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

A

45^o

B

180^o

C

0^o

D

90^o

Question 16: Palette 16/50

NEET 2016 MCQ

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?

A

Velocity is perpendicular to $\overrightarrow r $ and acceleration is directed towards the origin.

B

Velocity is perpendicular to $\overrightarrow r $ and acceleration is directed away from the origin.

C

Velocity and acceleration both are perpendicular to $\overrightarrow r $

D

Velocity and acceleration both are parallel to $\overrightarrow r $

Question 17: Palette 17/50

NEET 2015 MCQ

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

A

$t = {\pi \over \omega }$

B

t $=$ 0

C

$t = {\pi \over {4\omega }}$

D

$t = {\pi \over {2\omega }}$

Question 18: Palette 18/50

NEET 2015 MCQ

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?

A

Magnitude of the velocity of particle is 8 meter/second.

B

Path of the particle is a circle of radius 4 meter.

C

Acceleration vector is along $-$$\overrightarrow R $.

D

Magnitude of acceleration vector is ${{{v^2}} \over R}$
where v is the velocity of particle.

Question 19: Palette 19/50

NEET 2015 MCQ

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

A

$5\sqrt 2 $ h

B

$10\sqrt 2 $ h

C

0 h

D

5 h

Question 20: Palette 20/50

NEET 2014 MCQ

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)

A

3.5

B

5.9

C

16.3

D

110.8

Question 21: Palette 21/50

NEET 2014 MCQ

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

A

${1 \over 5}\left( {13\widehat i + 14\widehat j} \right)$

B

${7 \over 3}\left( {\widehat i + \widehat j} \right)$

C

$2\left( {\widehat i + \widehat j} \right)$

D

${11 \over 5}\left( {\widehat i + \widehat j} \right)$

Question 22: Palette 22/50

NEET 2013 MCQ

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

A

$\overrightarrow A \times \overrightarrow B $

B

$\overrightarrow B + \overrightarrow C $

C

$\overrightarrow B \times \overrightarrow C $

D

$\overrightarrow B $ and $\overrightarrow C $

Question 23: Palette 23/50

NEET 2013 MCQ

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

A

$2\widehat i - 3\widehat j$

B

$2\widehat i + 3\widehat j$

C

$-$$2\widehat i - 3\widehat j$

D

$-$$2\widehat i + 3\widehat j$

Question 24: Palette 24/50

NEET 2012 MCQ

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

A

$9\sqrt 2 $

B

$5\sqrt 2 $

C

5 units

D

9 units

Question 25: Palette 25/50

NEET 2012 MCQ

The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is

A

$\theta $ = tan^$-$1$\left( {{1 \over 4}} \right)$

B

$\theta $ = tan^$-$1(4)

C

$\theta $ = tan^$-$1(2)

D

$\theta $ = 45^o

Question 26: Palette 26/50

NEET 2011 MCQ

A projectile is fired at an angle of 45^o with the horizontal. Elevation angle of the projectile at its highest point as seen from the point of projection, is

A

45^o

B

60^o

C

tan^$-$1 $\left( {{1 \over 2}} \right)$

D

tan^$-$1 $\left( {{{\sqrt 3 } \over 2}} \right)$

Question 27: Palette 27/50

NEET 2011 MCQ

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

A

1 m/s²

B

7 m/s²

C

$\sqrt 7 $ m/s²

D

5 m/s²

Question 28: Palette 28/50

NEET 2011 MCQ

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

A

40 m

B

50 m

C

60 m

D

20 m

Question 29: Palette 29/50

NEET 2011 MCQ

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

A

15 m/s²

B

25 m/s²

C

36 m/s²

D

5 m/s²

Question 30: Palette 30/50

NEET 2010 MCQ

The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is

A

60^o

B

15^o

C

30^o

D

45^o

Question 31: Palette 31/50

NEET 2010 MCQ

A particle moves in x-y plane according to rule x = asin$\omega $t and y = acos$\omega $t. The particle follows

A

an elliptical path

B

a circular path

C

a parabolic path

D

a straight line path inclined equally to x and y-axes

Question 32: Palette 32/50

NEET 2010 MCQ

Six vectors, $\overrightarrow a $ through $\overrightarrow f $ have the magnitudes and directions indicated in the figure. Which of the following statements is true ?

A

$\overrightarrow b + \overrightarrow c = \overrightarrow f $

B

$\overrightarrow d + \overrightarrow c = \overrightarrow f $

C

$\overrightarrow d + \overrightarrow e = \overrightarrow f $

D

$\overrightarrow b + \overrightarrow e = \overrightarrow f $

Question 33: Palette 33/50

NEET 2010 MCQ

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

A

7 units

B

$7\sqrt 2 $ units

C

8.5 units

D

10 units

Question 34: Palette 34/50

NEET 2008 MCQ

A particle shows distance - time curve as given in this figure. The maximum instaneous velocity of the particle is around the point

A

D

B

A

C

B

D

C

Question 35: Palette 35/50

NEET 2007 MCQ

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

A

45^o

B

60^o

C

0^o

D

30^o.

Question 36: Palette 36/50

NEET 2007 MCQ

$\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

A

45^o

B

30^o

C

90^o

D

60^o

Question 37: Palette 37/50

NEET 2006 MCQ

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

A

45^o

B

90^o

C

60^o

D

75^o

Question 38: Palette 38/50

NEET 2006 MCQ

For angles of projection of a projectile at angle (45^o $-$ $\theta $) and (45^o + $\theta $), the horizontal range described by the projectile are in the ratio of

A

2 : 1

B

1 : 1

C

2 : 3

D

1 : 2.

Question 39: Palette 39/50

NEET 2005 MCQ

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

A

1/2

B

$-$ 1/2

C

1

D

$-$ 1.

Question 40: Palette 40/50

NEET 2005 MCQ

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

A

BA²sin$\theta $

B

BA²cos$\theta $

C

BA²sin$\theta $cos$\theta $

D

zero.

Question 41: Palette 41/50

NEET 2005 MCQ

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

A

${a \over {\sqrt {{v^2} + {v_1}^2} }}$

B

${a \over {v + {v_1}}}$

C

${a \over {v - {v_1}}}$

D

$\sqrt {{a \over {{v^2} - {v_1}^2}}} $

Question 42: Palette 42/50

NEET 2005 MSQ

A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revoluations in 44 seconds, what is the magnitude and direction of acceleration of the stone ?

A

${\pi ^2}\,$ m s^$-$2 and direction along the radius towards the centre

B

${\pi ^2}\,$ m s^$-$2 and direction along the radius away from the centre

C

${\pi ^2}\,$ m s^$-$2 and direction along the tangent to the circle

D

${\pi ^2}\,$/4 ms^$-$2 and direction along the radius towards the centre.

Question 43: Palette 43/50

NEET 2004 MCQ

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

A

(A² + b² + AB)^1/2

B

${\left( {{A^2} + {B^2} + {{AB} \over {\sqrt 3 }}} \right)^{1/2}}$

C

A + B

D

(A² + B² + ${\sqrt 3 }$AB)^1/2.

Question 44: Palette 44/50

NEET 2003 MCQ

The vector sum of two forces is perpendicular to their vector differences. In that case, the forces

A

are equal to each other

B

are equal to each other in magnitude

C

are not equal to each other in magnitude

D

cannot be predicted.

Question 45: Palette 45/50

NEET 2002 MCQ

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

A

particle A will reach at ground first with respect to particle B

B

particle B will reach at ground first with respect to particle A

C

both particles will reach at ground simultaneously

D

both particles will reach at ground with same speed.

Question 46: Palette 46/50

NEET 2001 MCQ

If $\left| {\overrightarrow A + \overrightarrow B } \right| = \left| {\overrightarrow A } \right| + \left| {\overrightarrow B } \right|$ then angle between A and B will be

A

90^o

B

120^o

C

0^o

D

60^o.

Question 47: Palette 47/50

NEET 2001 MCQ

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

A

${r \over R}$

B

${R \over r}$

C

1

D

$\sqrt {{R \over r}} $

Question 48: Palette 48/50

NEET 2000 MCQ

Two projectiles of same mass and with same velocity are thrown at an angle 60^o and 30^o with the horizontal, then which will remain same

A

time of flight

B

range of projectile

C

maximum height acquired

D

all of them.

Question 49: Palette 49/50

NEET 2000 MCQ

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

A

${v_B} > {v_m}$

B

${v_B} < {v_m}$

C

${v_B} = {v_m}$

D

${v_B}$ and ${v_m}$ can't be related.

Question 50: Palette 50/50

NEET 2000 MCQ

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

A

3 km/hr

B

4 km/hr

C

$\sqrt {29} $ km/hr

D

$\sqrt {41} $ km/hr.