MCQ of Motion in a Plane | Chapter 4 | Physics | Class 11 | CBSE |

MCQ of Motion in a Plane, Chapter 4, Class 11, Physics

Multiple Choice Questions of Motion in a Plane, Chapter 4, Class 11, Physics

 

Question 1: A vector is not changed if

  1. It is displaced parallel to itself
  2. It is rotated through an arbitrary angle
  3. It is cross multiplied a unit vector
  4. It is multiplied by an arbitrary scalar

Answer: A ( It is displaced parallel to itself )

Question 2: Which of the following is not a property of a null vector?

  1. A + 0 = A
  2. λ0 = 0, where λ is a scalar
  3. 0 A = A
  4. A – A = 0

Answer: C ( 0 A = A) 

Question 3: Two vectors A and B  inclined at an angle θ have a resultant R which makes an angle α with A . If the directions of A and B are interchanged, the resultant will have the same

  1. Direction
  2. Magnitude
  3. Direction as well as magnitude
  4. None of these 

Answer: B (Magnitude)

Question 4: A+ B+ C+ D = 0, which of the following statements is correct?

  1. A , B, C and D must equal be a null vector.
  2. The magnitude of ( A+ C) equal the magnitude of (B + D) .
  3. The magnitude of A can never be greater than the sum of magnitudes of  B, C and  D.
  4. B + C must lie in the plane of A and  D if A and D are not collinear and in the line of A and D, if they are collinear.

Answer: A ( A, B, C and D must equal be a null vector)

Question 5: The component of vector A = 2 î + 3 jˆ along the direction of ( î  – jˆ) is

  1. 1 / √2
  2. – 1 / √2
  3. 1 / 2
  4. –1 / 2

Answer: B ( –1 / √2)

Question 6: The magnitude of x component of vector A is 3 and the magnitude of vector A is 5. What is the magnitude of y component of vector A ?      

  1. 3
  2. 4
  3. 5
  4. 8

Answer: B (4)

Question 7: The direction cosines of î + jˆ + kˆ are

  1. 1,1,1
  2. 2,2,2
  3. 1 / √2,  1 / √2, 1 / √2
  4. 1 / √3,  1 / √3, 1 / √3

Answer: D ( 1 / √3, 1 / √3, 1 / √3)  

Question 8: If a vector A makes an angle α, β and γ respectively with the x,y and z axes respectively. Then is equal to

  1. 0
  2. 1
  3. 2
  4. 3

Answer: C (2)

Question 9: Which of the following quantities is dependent of the choice of orientation of the coordinate axis?

  1. A + B
  2. Ax + By
  3. | A+ B |
  4. Angle between A and B

Answer: B ( A x + B y)

Question 10: A unit vector in the direction of resultant vector of = -2 î + 3 jˆ + kˆ and = î + 2 jˆ – 4 kˆ is

  1. –2 î + 3 jˆ + kˆ/ √35
  2. î + 2 jˆ – 4 kˆ / √35
  3. –î + 5 jˆ – 3 kˆ / √35
  4. –3 î + jˆ + 5 kˆ / √ 35

Answer: C ( – î + 5 jˆ – 3 kˆ / √35)

You may also read MCQ of Physical World, MCQ of Units and Measurements, MCQ of Motion in a Straight LineMCQ of Laws of Motion, MCQ of Work, Energy and Power, MCQ of System of Particles and Rotational Motion, MCQ of Gravitation for better understanding of the chapters.

Question 11: The component of the sum of the two vectors 2 î + 3 jˆ and 2 jˆ + 3 kˆ along x and y direction respectivelty

  1. 2 and 5
  2. 4 and 6
  3. 2 and 6
  4. 4 and 3

Answer: A (2 and 5)

Question 12: The (x,y,z) coordinates of two points A and B are given respectively as (0,4,-2) and (-2,8,-4). The displacement vector from A to B is

  1. – 2 î + 4 jˆ– 2kˆ
  2. 2 î – 4 jˆ+ 2 kˆ
  3. 2 î + 4 jˆ – 2 kˆ
  4. –2 î – 4 jˆ – 2 kˆ

Answer: A ( –2 î + 4 jˆ – 2 kˆ)

Question 13: The position of a particle is given by r = 3t î + 2t2 jˆ + 5 kˆ, where t is in seconds and the coefficient have the proper units for r to be in metres. The direction of velocity of the particle at t = 1 s is

  1. 53° with x-axis
  2. 37° with x-axis
  3. 30º with y-axis
  4. 60° with y-axis

Answer: A ( 53° with x axis)

Question 14:Rain is falling vertically with a speed of 30 m s-1. A woman rides a bicycle with a speed of 12 m s-1 in east to west direction. In which direction she hold her umbrella?

  1. At an angle of tan-1(2/5) with the vertical towards the east
  2. At an angle of tan-1(2/5) with the vertical towards the west.
  3. At an angle of  tan-1(5/2) with the vertical towards the east
  4. At an angle of  tan-1(5/2) with vertical towards the west

Answer: B ( At an angle of tan-1(2/5) with the vertical towards the west)

Question 15: A river is flowing from west to east with a speed of 5 m s-1. A swimmer can swim in still water at speed of 10 m s-1. If he wants to start from point A on south bank and reach opposite point B on north bank, in what direction should he swim?

  1. 30° east of earth
  2. 60° east of north
  3. 30° west of north
  4. 60° west of north

Answer: C ( 30° west of north)

Question 16: Which of the following is true regarding projectile motion?

  1. Horizontal velocity of projectile is constant
  2. Vertical velocity of projectile is constant
  3. Acceleration is not constant
  4. Momentum is constant

Answer: A (Horizontal velocity of projectile is constant)

Question 17: A bomb is released by a horizontal flying aeroplane. The trajectory of bomb is

  1. A parabola
  2. A straight line
  3. A circle
  4. A hyperbola

Answer: A (A parabola)

Question 18: In case of projectile motion , what is the angle between the velocity and the acceleration of highest point?

  1. 45°
  2. 90°
  3. 180°

Answer: C (90°)

Question 19: If a body is projected with an angle θ to the horizontal, then

  1. Its velocity is always perpendicular to the acceleration
  2. Its velocity become zero at its maximum height
  3. Its velocity  makes zero angle with horizontal at its maximum height
  4. The body just before hitting the ground, the direction of velocity coincides with the acceleration

Answer: C ( Its velocity makes zero angle with horizontal at its maximum height)

Question 20: The relation between time of flight of projectile Tf and the time to reach the maximum height tm is 

  1. Tf = 2 tm
  2. Tf = tm
  3. Tf = tm / 2
  4. Tf = √2 (tm)

Answer: A (Tf = 2 tm)

Question 21: Two balls are projected at an angle θ and (90°– θ) to the horizontal with the same speed. The ratio of their vertical heights is

  1. 1 : 1
  2. tanθ : 1
  3. 1 : tanθ
  4. tan2θ : 1

Answer: D ()

Question 22: If R and H represent horizontal range and maximum height of the projectile ,then the angle of projection with the horizontal is

  1. tan-1(H/R)
  2. tan-1(2H/R)
  3. tan-1(4H/R)
  4. tan-1(4R/H)

Answer: C (tan-1(4H/R))

Question 23: 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?

  1. Range
  2. Maximum height
  3. Speed at which it strikes the ground
  4. The angle at which projectile strikes the ground

Answer: D (The angle at which projectile strikes the ground) 

Question 22: Two projectiles are fired from the same point with same speed at angles of projection of 60° and 30° respectively. Which of the following is true?

  1. Their range will be the same
  2. Their maximum height will be the same
  3. Their velocity at the highest point will be the same
  4. Their time of flight will be same

Answer: A (Their range will be  the same)

Question 23: A cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same speed how much high above the ground can the cricketer throw the same ball?

  1. 50 m
  2. 100 m
  3. 150 m
  4. 200 m

Answer: A (50 m )

Question 24: The speed of a projectile at its maximum height √3 / 2 times its initial speed. If the range of the projectile is P times the maximum height attained by it, then P equals

  1. 4 / 3
  2. 2√3
  3. 4√3
  4. 3 / 4 

Answer: C (4√3)

Question 25: Four bodies A, B, C and D are projected with equal speeds having angles of projection 15°, 30°, 45° and 60° with the horizontal respectively. The body having the shortest range is

  1. A
  2. B
  3. C
  4. D

Answer: A (A)

Question 26: Velocity vector and acceleration vector in a uniform circular motion are related as 

  1. Both in the same direction
  2. Perpendicular to each other
  3. Both in opposite direction
  4. Not related to each other

Answer: B (Perpendicular to each other)

Question 27: A body executing uniform circular motion has its position vector and acceleration vector

  1. Along the same direction
  2. In opposite direction
  3. Normal to each other
  4. Not related to each other

Answer: B (In opposite direction)

Question 28: For a particle performing a circular motion choose the incorrect statement from the following

  1. Magnitude of particle velocity (speed) remains constant
  2. Particle velocity remain directed perpendicular to radius vector
  3. Direction of acceleration keeps changing as particle moves
  4. Magnitude of acceleration does not remain constant

Answer: D (Magnitude of acceleration does not remain constant)

Question 29: Which of the following statement is incorrect?

  1. In one dimension motion, the velocity and the acceleration of an object always along the same line
  2. In two or three dimension, the angle between velocity and acceleration vectors may have any value between 0° and 180°.
  3. The kinematic equations for uniform acceleration can be applied in case of uniform circular motion
  4. The resultant acceleration of an object in circular motion is towards the centre only if the speed is constant 

Answer: C (The kinematic equations for uniform acceleration can be applied in case of uniform circular motion)

Question 30: An insect trapped in a circular groove of radius 12 cm moves along the groove steadily and completes 7 revolutions in 100 s. The linear speed of the insect is

  1. 4.3 cm s-1
  2. 5.3 cm s-1
  3. 6.3 cm s-1
  4. 7.3 cm s-1

Answer: B (5.3 cm s-1)

Question 31: Rain is falling vertically with a speed of 35 m s-1. Winds starts blowing after sometime with a speed of 12 ms-1 in east to west direction. At what angle with the vertical should a boy waiting at bus stop hold his umbrella to protect himself from rain?

  1. sin-1 (12 / 35)
  2. cos-1 (12 / 35)
  3. tan-1 (12 / 35)
  4. cot-1 (12 / 35)

Answer: C (tan-1 (12 / 35) )

Question 32: Which of the following statement is false regarding the vectors?

  1. The magnitude of vector is always scalar
  2. Each component of vector is always scalar
  3. Two vectors having different magnitude cannot have their resultant zero
  4. Vectors obey triangle law of vector addition

Answer: B (Each component of vector is always scalar)

Question 33: A river is flowing due east with a speed of 3 m s-1. A swimmer can swim in still water at a speed of 4 m s-1. If swimmer starts swimming due north, then resultant velocity of the swimmer is

  1. 3 m s-1
  2. 5 m s-1
  3. 7 m s-1
  4. 2 ms-1

Answer:  B (5 m s-1    

Question 34: Which of the following statements is true

  1. Scalar quantity is the one that is conserved in a process
  2. Scalar quantity is the one that can never take negative values
  3. Scalar quantity is the one that does not vary from one point to another in space
  4. Scalar quantity has the same value for observers with different orientation of the axes

Answer: D (Scalar quantity has the same value for observers with different orientation of the axes)

Question 35: When an object is shot from the bottom of a long smooth inclined plane kept at an angle 60° with horizontal it can travel a distance x1 along the plane. But when the inclination is decreased to 30° send the same object is shot with the same velocity it can travel x2 distance . Then x1: x2 will be

  1. 1 : 2√3
  2. 1 : √2
  3. √2 : 1
  4. 1 : √3

Answer: D (1 : √3)

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