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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 θ_{1}. In the next two seconds, it rotates through angle θ_{2}. 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^{-1}4.

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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