# NCERT Class 11 Physics Solutions: Chapter 4 – Motion in a Plane Part 10 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 4.23:

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

(a)

(b)

(c)

(d)

(e)

(The ‘average’ stands for average of the quantity over the time interval t1 to t2)

**Answer**: (b) and (e)

**Explanation**:

(a) : **False**:

It is given that the motion of the particle is arbitrary. Therefore, the average velocity of the particle cannot be given by this equation.

(b) : **True**

The arbitrary motion of the particle can be represented by this equation.

(c) : **False**:

The motion of the particle is arbitrary. The acceleration of the particle may also be non-uniform. Hence, this equation cannot represent the motion of the particle in space.

(d) : **False**:

The motion of the particle is arbitrary; acceleration of the particle may also be non-uniform. Hence, this equation cannot represent the motion of particle in space.

(e) : **True**

The arbitrary motion of the particle can be represented by this equation.

**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

**Answer**:

(a) Is conserved in a process: **False**

Despite being a scalar quantity, energy is not conserved in inelastic collisions.

(b) Can never take negative values: **False**

Despite being a scalar quantity, temperature can take negative values.

(c) Must be dimensionless: **False**

Total path length is a scalar quantity. Yet it has the dimension of length.

(d) Does not vary from one point to another in space: **False**

A scalar quantity such as gravitational potential can vary from one point to another in space.

(e) Has the same value for observers with different orientations of axes: **True**

The value of a scalar does not vary 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 30°, what is the speed of the aircraft?

**Answer**:

The positions of the observer and the aircraft are shown in the given figure:

Height of the aircraft from ground,

Angle subtended between the positions,

Time

In, :

is similar to

PQ = PR + RQ

∴ Speed of the aircraft