NCERT Solutions for Class 11 Physics Chapter 4 - Motion in a Plane

Question 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 velocity, displacement and angular frequency.

Question 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 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 and charge.

Question 4:

State with reasons, whether the following algebraic operations with scalars and vectors are meaningful :
Adding any two scalars

Question 5:

State with reasons, whether the following algebraic operations with scalars and vectors are meaningful :
Adding a scalar to a vector of the same dimensions

Question 6:

State with reasons, whether the following algebraic operations with scalars and vectors are meaningful :
Multiplying any vector by any scalar

Question 7:

State with reasons, whether the following algebraic operations with scalars and vectors are meaningful :
Multiplying any two scalars

Question 8:

State with reasons, whether the following algebraic operations with scalars and vectors are meaningful :
Adding any two vectors

Question 9:

State with reasons, whether the following algebraic operations with scalars and vectors are meaningful :
Adding a component of a vector to the same vector.

Question 10:

Read each statement below carefully and state with reasons, if it is true or false :
the magnitude of a vector is always a scalar

Question 11:

Read each statement below carefully and state with reasons, if it is true or false :
each component of a vector is always a scalar

Question 12:

Read each statement below carefully and state with reasons, if it is true or false :
the total path length is always equal to the magnitude of the displacement vector of a particle

Question 13:

Read each statement below carefully and state with reasons, if it is true or false :
the average speed of a particle (defined a total path length divided by the time taken to cover the path) is either greater than or equal to the magnitude of average velocity of the particle over the same interval of time.

Question 14:

Read each statement below carefully and state with reasons, if it is true or false :
three vectors not lying in a plane can never add up to give null vector.

Question 15:

Establish the following vector inequalities geometrically or otherwise :

When does the equality sign in above cases apply ?

Question 16:

Establish the following vector inequalities geometrically or otherwise :

When does the equality sign in above cases apply ?

Question 17:

Establish the following vector inequalities geometrically or otherwise :

When does the equality sign in above cases apply ?

Question 18:

Establish the following vector inequalities geometrically or otherwise :

When does the equality sign in above cases apply ?

Question 19:

Question 21:

Question 22:

Question 23:

Question 24:

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. 4.6. What is the magnitude of the displacement vector for each girl ? For which girl is this equal to the actual length of path skated ?

Question 25:

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 circum-ference, and returns to the centre along QO as shown. If the round trip takes 10 min, what is the (a) net displacement (b) average velocity and (c) average speed of the cyclist ?

Question 26:

On an open ground, a motorist follows a track that turns to his left by an angle of 60$°$ 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 27:

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 minutes.
What is the average speed of the taxi

Question 28:

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 minutes.
What is the magnitude of average velocity ? Are the two equal ?

Question 29:

Rain is falling vertically with a speed of 30 ms^–1 . A woman rides a bicycle with a speed of 10 ms^–1 in the north to south direction. What is the direction in which she should hold her umbrella ?

Question 30:

A man can swim with a speed of 4.0 km h^–1 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^–1 and he makes his strokes normal to the river current ? How far down the river does he go when he reaches the other bank ?

Question 31:

In a harbour, wind is blowing at the speed of 72 km h^–1 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^–1 to the north, what is the direction of the flag on the mast of the boat ?

Question 32:

In a harbour, wind is blowing at the speed of 72 km h^–1 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^–1 to the north, what is the direction of the flag on the mast of the boat ?

Question 33:

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 ms^–1 can go without hitting the ceiling of the hall ?

Question 34:

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 35:

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 36:

An aircraft executes a horizontal loop of radius 1.00 km with steady speed of 900 km h^–1. Compare its centripetal acceleration with the acceleration due to gravity.

Question 37:

Read the statement below carefully and state, with reasons, if it is true or false :
The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre.

Question 38:

Read the statement below carefully and state, with reasons, if it is true or false :
The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point.

Question 39:

Read the statement below carefully and state, with reasons, if it is true or false :
The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector.

Question 40:

Question 41:

What is the magnitude and direction of velocity of the particle at t = 2s ?

Question 42:

Question 43:

What is the speed of the particle at that time ?

Question 44:

Question 45:

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

Question 46:

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

Question 47:

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

Question 48:

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

Question 49:

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

Question 50:

Read each statement below carefully and state, with reasons and examples, if it is true or false : A scalar quantity is one that is conserved in a process

Question 51:

Read each statement below carefully and state, with reasons and examples, if it is true or false : A scalar quantity is one that can never take negative values

Question 52:

Read each statement below carefully and state, with reasons and examples, if it is true or false : A scalar quantity is one that must be dimensionless

Question 53:

Read each statement below carefully and state, with reasons and examples, if it is true or false : A scalar quantity is one that does not vary from one point to another in space

Question 54:

Read each statement below carefully and state, with reasons and examples, if it is true or false : A scalar quantity is one that has the same value for observers with different orientations of axes.

Question 54:

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 30$°$, what is the speed of the aircraft ?