**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
**

- It is displaced parallel to itself

- It is rotated through an arbitrary angle

- It is cross multiplied a unit vector

- 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?**

- A + 0 = A
- λ0 = 0, where λ is a scalar
- 0 A = A
- 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**

- Direction
- Magnitude
- Direction as well as magnitude
- None of these

^{Answer: B (Magnitude)}

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

- A , B, C and D must equal be a null vector.
- The magnitude of ( A+ C) equal the magnitude of (B + D) .
- The magnitude of A can never be greater than the sum of magnitudes of B, C and D.
- 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 / √2
- – 1 / √2
- 1 / 2
- –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 ? }**

- 3
- 4
- 5
- 8

^{Answer: B (4)}

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

- 1,1,1
- 2,2,2
- 1 / √2, 1 / √2, 1 / √2
- 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}**

- 0
- 1
- 2
- 3

^{Answer: C (2)}

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

**A + B**- A
_{x}+ B_{y } - | A+ B |
- 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**

- –2 î + 3 jˆ + kˆ/ √35
- î + 2 jˆ – 4 kˆ / √35
- –î + 5 jˆ – 3 kˆ / √35
- –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 Line, MCQ 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**

- 2 and 5
- 4 and 6
- 2 and 6
- 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**

- – 2 î + 4 jˆ– 2kˆ
- 2 î – 4 jˆ+ 2 kˆ
- 2 î + 4 jˆ – 2 kˆ
- –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 + 2t ^{2} 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**

- 53° with x-axis
- 37° with x-axis
- 30º with y-axis
- 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?**

- At an angle of tan
^{-1}(2/5) with the vertical towards the east - At an angle of tan
^{-1}(2/5) with the vertical towards the west. - At an angle of tan
^{-1}(5/2) with the vertical towards the east - 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?**

- 30° east of earth
- 60° east of north
- 30° west of north
- 60° west of north

^{Answer: C ( 30° west of north)}

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

- Horizontal velocity of projectile is constant
- Vertical velocity of projectile is constant
- Acceleration is not constant
- 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**

- A parabola
- A straight line
- A circle
- 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?**

- 0°
- 45°
- 90°
- 180°

^{Answer: C (90°)}

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

- Its velocity is always perpendicular to the acceleration
- Its velocity become zero at its maximum height
- Its velocity makes zero angle with horizontal at its maximum height
- 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 T _{f} and the time to reach the maximum height t_{m} is **

- T
_{f}= 2 t_{m} - T
_{f}= t_{m} - T
_{f}= t_{m}/ 2 - T
_{f}= √2 (t_{m})

^{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
- tanθ : 1
- 1 : tanθ
- tan
^{2}θ : 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**

- tan
^{-1}(H/R) - tan
^{-1}(2H/R) - tan
^{-1}(4H/R) - 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?**

- Range
- Maximum height
- Speed at which it strikes the ground
- 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 sam****e speed at angles of projection of 60° and 30° respectively. Which of the following is true?**

- Their range will be the same
- Their maximum height will be the same
- Their velocity at the highest point will be the same
- 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?**

- 50 m
- 100 m
- 150 m
- 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**

- 4 / 3
- 2√3
- 4√3
- 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**

- A
- B
- C
- D

**Answer: A (A)**

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

- Both in the same direction
- Perpendicular to each other
- Both in opposite direction
- 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**

- Along the same direction
- In opposite direction
- Normal to each other
- 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**

- Magnitude of particle velocity (speed) remains constant
- Particle velocity remain directed perpendicular to radius vector
- Direction of acceleration keeps changing as particle moves
- 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?**

- In one dimension motion, the velocity and the acceleration of an object always along the same line
- In two or three dimension, the angle between velocity and acceleration vectors may have any value between 0° and 180°.
- The kinematic equations for uniform acceleration can be applied in case of uniform circular motion
- 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**

- 4.3 cm s
^{-1} - 5.3 cm s
^{-1} - 6.3 cm s
^{-1} - 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?**

- sin
^{-1}(12 / 35) - cos
^{-1}(12 / 35) - tan
^{-1}(12 / 35) - cot
^{-1}(12 / 35)

**Answer: C (tan ^{-1} (12 / 35) )**

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

- The magnitude of vector is always scalar
- Each component of vector is always scalar
- Two vectors having different magnitude cannot have their resultant zero
- 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**

- 3 m s
^{-1} - 5 m s
^{-1} - 7 m s
^{-1} - 2 ms
^{-1}

**Answer: B (5 m s ^{-1}) **

**Question 34: ****Which of the following statements is true**

- Scalar quantity is the one that is conserved in a process
- Scalar quantity is the one that can never take negative values
- Scalar quantity is the one that does not vary from one point to another in space
- 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 : 2√3
- 1 : √2
- √2 : 1
- 1 : √3

**Answer: D (1 : √3)**

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