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Motion in a Plane Class 11 MCQs Questions with Answers
Multiple Choice Questions
Question 1.
Three vectors A, B and C satisfy the relation A.B = 0 and A.C = 0. The vector A is parallel to
(a) B
(b) C
(c) B × c
(d) B.C
Answer
Answer: (c) B × c
Question 2.
What is the minimum number of unequal forces whose resultant will be zero?
(a) 1
(b) 2
(c) 3
(d) 4
Answer
Answer: (c) 3
Question 3.
A body travelling in a circular path at uniform speed has :
(a) constant velocity
(b) tangential acceleration
(c) inward acceleration
(d) outward acceleration
Answer
Answer: (c) inward acceleration
Question 4.
When a disc containing mercury and water is rotated rapidly about a vertical axis, then the outermost place in the disc will be taken by:
(a) water
(b) mercury
(c) sometimes water and sometimes mercury
(d) none of these.
Answer
Answer: (b) mercury
Question 5.
The resultant of two forces P and Q is R. If one of the forces is reversed in direction, then the resultant becomes S. Then for the identity R² + S² = 2(P² + Q²) to hold good
(a) The forces are collinear
(b) The forces act as right angles to each other
(c) The forces are inclined at 45° to each other
(d) The forces can have any angle of inclination between them
Answer
Answer: (d) The forces can have any angle of inclination between them
Question 6.
A bus is moving on a straight road towards north with a uniform speed of 50 kmh-1 when it turns left through 90°. If the speed remains unchanged after turning, the increase in the velocity of the bus in the turning process is :
(a) zero
(b) 50 kmh-1
(c) 70.7 kmh-1 along south-west direction
(d) 70.7 lcmh-1 along north-west direction
Answer
Answer: (c) 70.7 kmh-1 along south-west direction
Question 7.
Two bullets are fired simultaneously horizontally and with different speeds from the same place. Which bullet will hit the ground first?
(a) The slower one
(b) The faster one
(c) Both will reach simultaneously
(d) Depends on the masses
Answer
Answer: (c) Both will reach simultaneously
Question 8.
A particle is acted upon by a force of constant magnitude, which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that:
(a) its velocity is constant
(b) its acceleration is constant
(c) its kinetic energy is constant
(d) it moves in a circular path
Answer
Answer: (c) and (d).
Question 9.
The muzzle speed of a certain rifle is 330 ms-1. At the end of one second, a bullet fired straight up into the air will travel a distance of:
(a) 330 m
(b) (330 – 4.9) m
(c) (330 – 9.8) m
(d) (330 + 4.9) m
Answer
Answer: (b) (330 – 4.9) m
Question 10.
If a body A of mass M is thrown with velocity v at angle of 30° to the horizontal and another body B of the same mass is thrown with the same speed at an angle of 60° to the horizontal, the ratio of the horizontal ranges of A and B will be
(a) 1 : 3
(b) 1 : 1
(c) √3 : 1
(c) 1 : √3
Answer
Answer: (b) 1 : 1
Question 11.
One body is dropped while a second body is thrown downwards with an initial velocity of 1 ms-1 simultaneously. The separation between these is 18 m after a time
(a) 4.5 s
(b) 9 s
(c) 18 s
(d) 36 s
Answer
Answer: (c) 18 s
Question 12.
A boat which has the speed of 5 kmh-1 still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water is
(a) 3 kmh-1
(b) 4 kmh-1
(c) \(\sqrt {41}\) kmh-1
(d) 1 kmh-1
Answer
Answer: (a) 3 kmh-1
Question 13.
Which of the following vectors is perpendicular to \(\hat {i}\) Pcos 9 +
(a) \(\hat {i}\) Pcos θ + \(\hat {j}\) Qsin θ
(b) \(\hat {i}\) Qcos θ – \(\hat {j}\) Psin θ
(c) \(\hat {i}\) Psin θ + \(\hat {j}\) Qcos θ
(d) \(\hat {i}\) Qsin θ – \(\hat {j}\)Pcos θ
Answer
Answer: (d) \(\hat {i}\) Qsin θ – \(\hat {j}\)Pcos θ
Question 14.
Which of the following operations between the two vectors can yield a vector perpendicular to either of them
(a) addition
(b) subtraction
(c) multiplication
(d) division
Answer
Answer: (c) multiplication
Question 15.
Which of the following is the essential characteristic of a projectile?
(a) Zero velocity at the highest point
(b) Initial velocity inclined to the horizontal
(c) Constant acceleration perpendicular to the velocity
(d) None of these
Answer
Answer: (d) None of these
Question 16.
A projectile is projected with a linear momentum p making angle θ with the horizontal. The change in momentum of the projectile on return to the ground will be
(a) 2p
(b) 2p sin θ
(c) 2p tan θ
(d) 2p cos θ
Answer
Answer: (b) 2p sin θ
Question 17.
A ball is projected from the top of a tower at an angle of 60° with the vertical. What happens to the vertical component of its velocity?
(a) increases continuously
(b) decreases continuously
(c) remains unchanged
(d) first decreases and then increases
Answer
Answer: (d) first decreases and then increases
Question 18.
A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first two seconds, it rotates through angle θ1. In the next two seconds, it rotates through angle θ2. What is the ratio \(\frac {θ_2}{θ_1}\)
(a) 1
(b) 2
(c) 3
(d) 4
Answer
Answer: (c) 3
Question 19.
Which of the following remains constant for a projectile fired from the Earth?
(a) kinetic energy
(b) momentum
(c) horizontal component of velocity
(d) vertical component of velocity
Answer
Answer: (c) horizontal component of velocity
Question 20.
Which of the following is the largest, when the height attained by the projectile is the greatest?
(a) range
(b) time of flight (T)
(c) angle of projectile with
(d) none of these the vertical
Answer
Answer: (b) time of flight (T)
Question 21.
The angle between \(\hat {P}\) and \(\hat {Q}\) is θ. What is |\(\hat {P}\)×\(\hat {Q}\)|?
(a) sin θ
(b) PQ sin θ
(c) PQ
(d) PQ cos θ
Answer
Answer: (a) sin θ
Question 22.
There are N coplanar vectors each of magnitude V. Each vector is inclined to the preceeding vector at angle\(\frac {2π}{N}\). What is the
magnitude of their resultant?
(a) NV
(b) V
(c) \(\frac {V}{N}\)
(d) Zero
Answer
Answer: (d) Zero
Question 23.
Out of the following which is not a scalar quantity?
(a) Time
(b) Volume
(c) Density
(d) Momentum
Answer
Answer: (d) Momentum
Question 24.
A particle is moving eastward with a velocity of 5 ms-1. In 10 seconds, the velocity changes to 5 ms-1 northward. The average acceleration in this time is
(a) zero
(b) \(\frac {1}{√2}\) ms-2 towards north
(c) \(\frac {1}{√2}\) ms-2 towards north-east
(d) \(\frac {1}{√2}\) ms-2 towards north-west
Answer
Answer: (d) \(\frac {1}{√2}\) ms-2 towards north-west
Question 25.
The following forces are acting on a particle
(i) (2\(\hat {i}\) + 3\(\hat {j}\) – 2\(\hat {k}\)) N
(ii) (3\(\hat {i}\) + \(\hat {j}\) – 3\(\hat {k}\))N
(iii) (-5\(\hat {i}\) – 2\(\hat {j}\) + \(\hat {k}\))N
the particle will move in
(a) x-y plane
(b) x-z plane
(c) y-z plane
(d) aong x-axis
Answer
Answer: (c) y-z plane
Fill in the blanks
Question 1
……………. is the maximum number of rectangular components into which a vector can be split in its own plane.
Answer
Answer: Two.
Question 2.
If \(\vec {A}\).\(\vec {B}\) = AB, then …………….. is the angle between \(\vec {A}\) and \(\vec {B}\).
Answer
Answer: zero.
Question 3.
If \(\vec {A}\)×\(\vec {B}\) = AB, then …………….. is the angle between \(\vec {A}\) and \(\vec {B}\).
Answer
Answer: \(\frac {π}{2}\)
Question 4.
When a ball is projected upwards, then its acceleration at the highest point is equal to …………….. and is directed ……………..
Answer
Answer: acceleration due to gravity, downward.
Question 5.
The horizontal range of the projectile is maximum when the angle of projection is ……………..
Answer
Answer: 45°.
Question 6.
…………….. should be the angle of projection so that the horizontal range is equal to the maximum height.
Answer
Answer: tan-14.
Question 7.
A particle covers equal distances around a circular path in equal intervals of time. It has uniform non zero rate of change of ……………..
Answer
Answer: angular displacement.
Question 8.
…………….. is the angle between instantaneous velocity and acceleration for a particle moving along a circular path with uniform speed.
Answer
Answer: \(\frac {π}{2}\)
Question 9.
Linear velocity, momentum and centripetal acceleration have their magnitude unchanged during circular motion but their …………….. changes from point to point.
Answer
Answer: direction.
Question 10.
Time of ascent and time of descent are always …………….. for a projectile fixed at some angle with the horizontal.
Answer
Answer: equal.
True/False Type Questions
Question 1.
The radial component of acceleration of a particle in circular motion is given by \(\frac {v^2}{r}\) (in magnitude) even when the speed v is not constant.
Answer
Answer: True
Question 2.
The unit vectors \(\hat {i}\) and \(\hat {j}\) along X and Y axis change with time.
Answer
Answer: False
Question 3.
If A.B = A.C then B = C.
Answer
Answer: True
Question 4.
Area is a scalar quantity.
Answer
Answer: False
Question 5.
Moment of inertia of body about an axis is a vector quantity.
Answer
Answer: False
Question 6.
The resultant of two coplanar vectors is also a coplanar vector.
Answer
Answer: True
Question 7.
A null vector has not direction.
Answer
Answer: True
Question 8.
The resultant of two vectors obtained by using triangle law and parallelogram law of vector addition will be different.
Answer
Answer: False
Question 9.
The horizontal component of velocity changes with time.
Answer
Answer: False
Question 10.
The vertical component of velocity changes with time.
Answer
Answer: True
Question 11.
The range depends only on the angle of elevation.
Answer
Answer: False
Question 12.
The time of flight depends only on initial velocity.
Answer
Answer: True
Question 13.
The time of flight depends only on the vertical component of initial velocity.
Answer
Answer: False
Question 14.
Linear velocity is uniform when angular velocity is uniform.
Answer
Answer: False
Question 15.
Magnitude of acceleration is constant.
Answer
Answer: True
Question 16.
Acceleration is directed along the tangent to the circular path.
Answer
Answer: False
Question 17.
Linear velocity always acts tangentially.
Answer
Answer: True
In a projectile motion, the velocity vector of the projectile is:
Question 18.
always perpendicular to the acceleration.
Answer
Answer: False
Question 19.
never perpendicular to the acceleration.
Answer
Answer: False
Question 20.
perpendicular to the acceleration only once during its flight.
Answer
Answer: True
Question 21.
perpendicular to the acceleration two times during its flight.
Answer
Answer: False
A ball is rolled off aong the edge of a horizontal table with velocity 4 ms-1. It hits the ground after time 0.4 s.
Question 22.
The height of the table is 0.8 m.
Answer
Answer: False
Question 23.
It hits the ground at angle of 60° with the vertical.
Answer
Answer: True
Question 24.
It hits the ground with a vertical velocity 4 ms-1.
Answer
Answer: False
Question 25.
It covers a horizontal distance 1.6 m from the table.
Answer
Answer: False.
Question 26.
A particle covers equal distances around a circular path in equal intervals of time. It has uniform non-zero rate of change of angular displacement.
Answer
Answer: True
Question 27.
The speed of the particle in part (a) remains constant with time.
Answer
Answer: True
Question 28.
A particle describing circular path of radius 10 m every 2s has average angular speed during 4s equal to π rad s-1.
Answer
Answer: True
Question 29.
Velocity determines the nature of the path followed by a particle.
Answer
Answer: True
Question 30.
Time of flight is the largest when the height attained by the projectile is the greatest.
Answer
Answer: True
Question 31.
Horizontal component of velocity of a projectile fired from the earth always remains constant.
Answer
Answer: True
Question 32.
Maximum height attained by the projectile is not affected by the mass of the projectile.
Answer
Answer: True
Question 33.
For maximum horizontal range R, the maximum height attained by the projectile is \(\frac {R}{4}\)
Answer
Answer: True
For three forces to produce zero resultant.
Question 34.
They should be in the same plane.
Answer
Answer: True
Question 35.
They should act along the sides of a parallelogram.
Answer
Answer: False
Question 36.
The resultant of any two forces should be equal and opposite to the third force.
Answer
Answer: True
Question 37.
It should be possible to represent them by the three sides of a triangle taken in the same order.
Answer
Answer: True
Question 38.
The components of a vector may be less than its magnitude.
Answer
Answer: True
Question 39.
The components of a vector may be equal to its magnitude.
Answer
Answer: True
Question 40.
The unit vector has unit magnitude and acts in the direction of given vector.
Answer
Answer: True
Question 41.
Null vector acts in arbitrary.
Answer
Answer: True
Question 42.
If |A×B| = AB, then angle between A and B is zero.
Answer
Answer: False
Question 43.
For two vectors to be parallel to each other; the cross product is always zero.
Answer
Answer: True
Question 44.
For two vectors to be perpendicular to each other, the dot product is always zero.
Answer
Answer: True
Question 45.
The resultant of two vectors of same magnitude always bisects the angle between them.
Answer
Answer: True
Question 46.
The maximum number of rectangular components of a given vector into which it can be split in own plane is two.
Answer
Answer: True
Question 47.
The maximum number of rectangular components of a given vector into which it can be split in space is three.
Answer
Answer: True
Question 48.
If \(\vec {A}\).\(\vec {B}\) = AB, then angle between \(\vec {A}\) and \(\vec {B}\) is \(\frac {π}{2}\).
Answer
Answer: False
Match Type Questions
| Column I | Column II |
| (a) Angular momentum | (i) horizontal |
| (b) Kinetic energy | (ii) is perpendicular to the acceleration only once during its flight |
| (c) The resultant of a number of coplanar forces acting at a point is | (iii) vector quantity |
| (d) The direction of motion of a projectile at the highest point of its trajectory is | (iv) Scalar quantity |
| (e) The velocity vector of the projectile in a projectile motion is | (v) the single force that produces the same effect |
| (f) An object is dropped through the window of a fast running train, then | (vi) to a man standing near its track, the path of object must be a parabola |
| (g) When milk is churned, cream separate out because of | (vii) A² |
| (h) A.A = | (viii) 3 |
| (i) Minimum number of unequal forces having zero resultant is | (ix) centrifugal force |
| (j) Acceleration of a body moving with constant speed in a circle is | (x) rω² |
Answer
Answer:
| Column I | Column II |
| (a) Angular momentum | (iii) vector quantity |
| (b) Kinetic energy | (iv) Scalar quantity |
| (c) The resultant of a number of coplanar forces acting at a point is | (v) the single force that produces the same effect |
| (d) The direction of motion of a projectile at the highest point of its trajectory is | (i) horizontal |
| (e) The velocity vector of the projectile in a projectile motion is | (ii) is perpendicular to the acceleration only once during its flight |
| (f) An object is dropped through the window of a fast running train, then | (vi) to a man standing near its track, the path of object must be a parabola |
| (g) When milk is churned, cream separate out because of | (ix) centrifugal force |
| (h) A.A = | (vii) A² |
| (i) Minimum number of unequal forces having zero resultant is | (viii) 3 |
| (j) Acceleration of a body moving with constant speed in a circle is | (x) rω² |
| Column I | Column II |
| (a) Dot product of two vectors is zero | (i) parallel vectors |
| (b) The cross product of two vectors is zero | (ii) perpendicular vectors |
| (c) Null vector | (iii) magnitude one |
| (d) unit vector | (iv) arbitrary direction |
Answer
Answer:
| Column I | Column II |
| (a) Dot product of two vectors is zero | (ii) perpendicular vectors |
| (b) The cross product of two vectors is zero | (i) parallel vectors |
| (c) Null vector | (iv) arbitrary direction |
| (d) unit vector | (iii) magnitude one |
| Column I | Column II |
| (a) Scalar | (i) both magnitude and direction |
| (b) Vectors | (ii) magnitude only |
| (c) Negative vectors | (iii) having common initial point |
| (d) Co-initial vectors | (iv) have equal magnitude but act in the opposite directions |
Answer
Answer:
| Column I | Column II |
| (a) Scalar | (ii) magnitude only |
| (b) Vectors | (i) both magnitude and direction |
| (c) Negative vectors | (iv) have equal magnitude but act in the opposite directions |
| (d) Co-initial vectors | (iii) having common initial point |
| Column I | Column II |
| (a) Resultant of two vectors is maximum | (i) scalar quantity |
| (b) Resultant of two vectors is minimum | (ii) vector quantity |
| (c) Cross product | (iii) 180° |
| (d) Dot product | (iv) 0° |
Answer
Answer:
| Column I | Column II |
| (a) Resultant of two vectors is maximum | (iv) 0° |
| (b) Resultant of two vectors is minimum | (iii) 180° |
| (c) Cross product | (ii) vector quantity |
| (d) Dot product | (i) scalar quantity |
| Column I | Column II |
| (a) Division of two vectors | (i) zero |
| (b) Equal magnitude and same direction | (ii) algebriacally |
| (c) Angle between two equal vectors | (iii) not allowed |
| (d) Vectors cannot be added or subtracted | (iv) equal vectors |
Answer
Answer:
| Column I | Column II |
| (a) Division of two vectors | (iii) not allowed |
| (b) Equal magnitude and same direction | (iv) equal vectors |
| (c) Angle between two equal vectors | (i) zero |
| (d) Vectors cannot be added or subtracted | (ii) algebriacally |
| Column I | Column II |
| (a) Vertical component of velocity is zero | (i) tangential to the circular path |
| (b) Angle of projection for maximum horizontal range | (ii) along the radius of circle and towards its centre |
| (c) Linear velocity | (iii) at the highest point of trajectory |
| (d) Centripetal acceleration | (iv) 45° |
Answer
Answer:
| Column I | Column II |
| (a) Vertical component of velocity is zero | (iii) at the highest point of trajectory |
| (b) Angle of projection for maximum horizontal range | (iv) 45° |
| (c) Linear velocity | (i) tangential to the circular path |
| (d) Centripetal acceleration | (ii) along the radius of circle and towards its centre |
| Column I | Column II |
| (a) A device used to separate light particles in suspen-sion from the more dense liquid | (i) 0° |
| (b) Angle of projection for a projectile thrown parallel to the horizontal | (ii) 0 |
| (c) Horizontal component of acceleration of a body thrown horizontally with uniform speed | (ii) g |
| (d) Vertical component of acceleration of a body thrown horizontally with uniform speed | (iv) centrifuge |
Answer
Answer:
| Column I | Column II |
| (a) A device used to separate light particles in suspen-sion from the more dense liquid | (iv) centrifuge |
| (b) Angle of projection for a projectile thrown parallel to the horizontal | (i) 0° |
| (c) Horizontal component of acceleration of a body thrown horizontally with uniform speed | (ii) 0 |
| (d) Vertical component of acceleration of a body thrown horizontally with uniform speed | (ii) g |
| Column I | Column II |
| (a) Three vectors having zero resultant must be | (i) bisects the angle between them |
| (b) Resultant of two equal vectors acting perpendicular to each other | (ii) co-planer |
| (c) A×B acts in a direction | (iii) perpendicular to the plane of A and B |
Answer
Answer:
| Column I | Column II |
| (a) Three vectors having zero resultant must be | (ii) co-planer |
| (b) Resultant of two equal vectors acting perpendicular to each other | (i) bisects the angle between them |
| (c) A×B acts in a direction | (iii) perpendicular to the plane of A and B |
| Column I | Column II |
| (a) In circular motion the centripetal accelearion | (i) inward radial acceleration |
| (b) In uniform circular motion, the velocity vector of the particle | (ii) remains constant in magnitude only |
| (c) Cream separation out of milk on churning takes place due to | (iii) centrifugal force |
| (d) A body travelling in a circular path at uniform speed has | (iv) changes in direction |
Answer
Answer:
| Column I | Column II |
| (a) In circular motion the centripetal accelearion | (ii) remains constant in magnitude only |
| (b) In uniform circular motion, the velocity vector of the particle | (iv) changes in direction |
| (c) Cream separation out of milk on churning takes place due to | (iii) centrifugal force |
| (d) A body travelling in a circular path at uniform speed has | (i) inward radial acceleration |
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