NCERT Solutions Class 11 Physics Chapter 4 Motion In A Plane Download In Pdf

Chapter 4 Motion In A Plane Download in pdf

**Question 4.1** State, for each of the following physical quantities, if it is a scalar or a vector :
volume, mass, speed, acceleration, density, number of moles, velocity, angular
frequency, displacement, angular velocity.

**Question 4.2 **Pick out the two scalar quantities in the following list :
force, angular momentum, work, current, linear momentum,electric field, average
velocity, magnetic moment, relative velocity.

**Question 4.3** Pick out the only vector quantity in the following list :
Temperature, pressure, impulse, time, power, total path length, energy, gravitational
potential, coefficient of friction, charge.

**Question 4.4** State with reasons, whether the following algebraic operations with scalar and vector
physical quantities are meaningful :

(a) adding any two scalars,

(b) adding a scalar to a vector of the same dimensions ,

(c) multiplying any vector by any scalar,

(d) multiplying any two scalars,

(e) adding any
two vectors,

(f) adding a component of a vector to the same vector.

**Question 4.5 **Read each statement below carefully and state with reasons, if it is true or false :

(a) The magnitude of a vector is always a scalar,

(b) each component of a vector is
always a scalar,

(c) the total path length is always equal to the magnitude of the
displacement vector of a particle. (

d) the average speed of a particle (defined as total
path length divided by the time taken to cover the path) is either greater or equal to
the magnitude of average velocity of the particle over the same interval of time,

(e)
Three vectors not lying in a plane can never add up to give a null vector.

**Question 4.6** Establish the following vector inequalities geometrically or otherwise :

(a) |a+b| < |a| + |b|

(b) |a+b| > ||a| âˆ’|b||

(c) |aâˆ’b| < |a| + |b|

(d) |aâˆ’b| > ||a| âˆ’ |b||

When does the equality sign above apply?

**Question 4.7** Given a + b + c + d = 0, which of the following statements
are correct :

(a) a, b, c, and d must each be a null vector,

(b) The magnitude of (a + c) equals the magnitude of
( b + d),

(c) The magnitude of a can never be greater than the
sum of the magnitudes of b, c, and d,

(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 ?

**Question 4.8** Three girls skating on a circular ice ground of radius
200 m start from a point P on the edge of the ground
and reach a point Q diametrically opposite to P following
different paths as shown in Fig. 4.20. What is the
magnitude of the displacement vector for each ? For
which girl is this equal to the actual length of
path skate ?

**Question 4.9 **A cyclist starts from the centre O of a circular park of radius 1 km, reaches the edge P
of the park, then cycles along the circumference, and returns to the centre along QO
as shown in Fig. 4.21. If the round trip takes 10 min, what is the (a) net displacement,
(b) average velocity, and (c) average speed of the cyclist ?

**Question 4.10** On an open ground, a motorist follows a track that turns to his left by an angle of 600
after every 500 m. Starting from a given turn, specify the displacement of the motorist
at the third, sixth and eighth turn. Compare the magnitude of the displacement with
the total path length covered by the motorist in each case .

**Question 4.11** A passenger arriving in a new town wishes to go from the station to a hotel located
10 km away on a straight road from the station. A dishonest cabman takes him along
a circuitous path 23 km long and reaches the hotel in 28 min. What is (a) the average
speed of the taxi, (b) the magnitude of average velocity ? Are the two equal ?

**Question 4.12** Rain is falling vertically with a speed of 30 m s-1. A woman rides a bicycle with a speed
of 10 m s-1 in the north to south direction. What is the direction in which she should
hold her umbrella ?

**Question 4.13** A man can swim with a speed of 4.0 km/h in still water. How long does he take to
cross a river 1.0 km wide if the river flows steadily at 3.0 km/h and he makes his reaches the other bank ?

**Question 4.14** In a harbour, wind is blowing at the speed of 72 km/h and the flag on the mast of a boat
anchored in the harbour flutters along the N-E direction. If the boat starts moving at a
speed of 51 km/h to the north, what is the direction of the flag on the mast of the boat ?

**Question 4.15** The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that
a ball thrown with a speed of 40 m s-1 can go without hitting the ceiling of the hall ?

**Question 4.16** A cricketer can throw a ball to a maximum horizontal distance of 100 m. How much
high above the ground can the cricketer throw the same ball ?

**Question 4.17 **A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a
constant speed. If the stone makes 14 revolutions in 25 s, what is the magnitude and
direction of acceleration of the stone ?

**Question 4.18 **An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900
km/h. Compare its centripetal acceleration with the acceleration due to gravity.

**Question 4.19** Read each statement below carefully and state, with reasons, if it is true or false :

(a) The net acceleration of a particle in circular motion is always along the radius of
the circle towards the centre

(b) The velocity vector of a particle at a point is always along the tangent to the path
of the particle at that point

(c) The acceleration vector of a particle in uniform circular motion averaged over one
cycle is a null vector

**Question 4.20** The position of a particle is given by
r = 3.0t Ë†i âˆ’ 2.0t 2 Ë†j + 4.0 kË† m
where t is in seconds and the coefficients have the proper units for r to be in metres.

(a) Find the v and a of the particle?

(b) What is the magnitude and direction of
velocity of the particle at t = 2.0 s ?

**Question 4.21** A particle starts from the origin at t = 0 s with a velocity of 10.0 j m/s and moves in
the x-y plane with a constant acceleration of + j) m s-2.

(a) At what time is
the x- coordinate of the particle 16 m? What is the y-coordinate of the particle at
that time?

(b) What is the speed of the particle at the time ?

**Question 4.22 **j are unit vectors along x- and y- axis respectively. What is the magnitude
and direction of the vectors ij ? What are the com along the directions [You may use graphical

method]

**Question 4.23** For any arbitrary motion in space, which of the following relations are true :

(a) vaverage = (1/2) (v (t1) + v (t2))

(b) v average = [r(t2) - r(t1) ] /(t2 â€“ t1)

(c) v (t) = v (0) + a
t

(d) r (t) = r (0) + v (0) t + (1/2) a t2

(e) a average =[ v (t2) - v (t1 )] /( t2 â€“ t1)

(The â€˜averageâ€™ stands for average of the quantity over the time interval t1 to t2)

**Question 4.24** Read each statement below carefully and state, with reasons and examples, if it is
true or false :
A scalar quantity is one that

(a) is conserved in a process

(b) can never take negative values

(c) must be dimensionless

(d) does not vary from one point to another in space

(e) has the same value for observers with different orientations of axes.

**Question 4.25 **An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at
a ground observation point by the aircraft positions 10.0 s apart is 30Â°, what is the
speed of the aircraft ?

**Question 4.26** A vector has magnitude and direction. Does it have a location in space ? Can it vary
with time ? Will two equal vectors a and b at different locations in space necessarily
have identical physical effects ? Give examples in support of your answer.

**Question 4.27** A vector has both magnitude and direction. Does it mean that anything that has
magnitude and direction is necessarily a vector ? The rotation of a body can be specified
by the direction of the axis of rotation, and the angle of rotation about the axis. Does
that make any rotation a vector ?

**Question 4.28** Can you associate vectors with (a) the length of a wire bent into a loop, (b) a plane
area, (c) a sphere ? Explain.

**Question 4.29** A bullet fired at an angle of 30Â° with the horizontal hits the ground 3.0 km away. By
adjusting its angle of projection, can one hope to hit a target 5.0 km away ? Assume
the muzzle speed to the fixed, and neglect air resistance.

**Question 4.30 **A fighter plane flying horizontally at an altitude of 1.5 km with speed 720 km/h passes
directly overhead an anti-aircraft gun. At what angle from the vertical should the gun
be fired for the shell with muzzle speed 600 m s-1 to hit the plane ? At what minimum
altitude should the pilot fly the plane to avoid being hit ? (Take g = 10 m s-2 ).

**Question 4.31** A cyclist is riding with a speed of 27 km/h. As he approaches a circular turn on the
road of radius 80 m, he applies brakes and reduces his speed at the constant rate of
0.50 m/s every second. What is the magnitude and direction of the net acceleration of
the cyclist on the circular turn ?

**Question 4.32** (a) Show that for a projectile the angle between the velocity and the x-axis as a function
of time is given by
( ) âˆ’
ox
0y
v
v gt
Î¸ t = tan-1 (b) Shows that the projection angle Î¸0 for a projectile launched from the origin is
given by
0 R
4h
Î¸ = tan-1 m
where the symbols have their usual meaning

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- Chapter 1 Physical World
- Chapter 2 Units And Measurement
- Chapter 3 Motion In A Straight Line
- Chapter 4 Motion In A Plane
- Chapter 5 Laws Of Motion
- Chapter 7 Systems of Particles and Rotational Motion
- Chapter 6 Work Energy and Power
- Chapter 8 Gravitation
- Chapter 9 Mechanical Properties Of Solids
- Chapter 10 Mechanical Properties Of Fluids
- Chapter 11 Thermal Properties of Matter
- Chapter 12 Thermodynamics
- Chapter 13 Kinetic Theory
- Chapter 14 Oscillations
- Chapter 15 Waves

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