Two Marks Questions with Answers

Part – ‘A'

‘2’ Marks Questions with Answers

1. Define multiparticle dynamics.

The study of dynamics of a system which consists of two or more particles is known multiparticle dynamics.

2. Define centre of mass of the system.

Consider the motion of a system consisting of a large number of particles. There is one point in it which behaves as though the entire mass of the system were concentrated there and all the external forces were acting at this point. This point is called the centre of mass of the system.

3. What is centre of mass (CM)?

A point in the system at which whole mass of the body is supposed to be concentrated is called centre of mass of the body.

4. Give the example for motion of centre of mass.

Examples for motion of centre of mass 

(i) Motion of planets and its satellite 

(ii) Projectile Trajectory 

(iii) Decay of a Nucleus

5. How centre of mass is determined for rigid body and regular shape? 

Centre of mass of some regular objects.

• For a rigid body, the centre of mass is a point at a fixed position with respect to the body as a whole. Depending on the shape of the body and the way the mass is distributed in it, the centre of mass is a point may or may not be within the body.

• If the shape is symmetrical and the mass distribution is uniform, we can usually find the location of the centre of mass quite easily.

• For a long thin rod of uniform cross section and density, the centre of mass is at the geometrical centre.

• For a thin circular plane ring, It is again at the geometrical centre of the circle. 

• For a rectangle, again the centre of mass is at the geometrical centre.

6.. What is the difference between centre of gravity and centre of mass?

• The centre of gravity of a body is a point, where the whole weight of the body is supposed to be concentrated.

• The centre of mass of a body is that point, where the whole mass of the body is supposed to be concentrated.

For uniform geometrically shaped, bodies the centre of gravity coincides with centre of mass. However, they do not coincide in bodies whose density is not uniform throughout.

7. Define rigid body.

A rigid body is defined as that body which does not undergo any change in shape or volume when external forces are applied on it.

8. Define rigid body rotation.

When a body rotates about a fixed axis, its motion is known as rotatory motion.

A rigid body is said to have pure rotational motion, if every particle of the body moves in a circle, the centre of which lies on a straight line is called the axis of rotation (Fig).

9. Write down the equation of motion for rotational motion.

10. Define moment of inertia of a body.

The property of a body by which it resists change in uniform rotational motion is called rotational inertia or moment of inertia.

11. Define moment of inertia of a particle

The moment of inertia of a particle about an axis is defined as the product of the mass of the particle and square of the distance of the particle from the axis of rotation.

If 'm' is the mass of the particle and ‘r’ is the distance of the particle from the axis of rotation, then

The moment of inertia of the particle

12. Define moment of inertia of a rigid body.

The moment of inertia of a rigid body about a given axis is the sum of products of masses of its particles and the square of their respective distances from the axis of rotation.

13. What are the factors the moment of inertia depends on?

Moment of inertia depends on mass, distribution of mass and on the position of axis of rotation.

14. What are the physical significance of moment of inertia?

The property which opposes the change in rotational motion of the body is called the moment of inertia. Greater is moment of inertia of the body about the axis of rotation, greater is the torque required to rotate the body.

Thus it is clear that the moment of inertia of a body has the same role in rotational motion as that of mass (or inertia) is linear motion.

15. What is radius of gyration?

The radius of gyration is defined as the distance from the axis of rotation to the point where the entire mass of the body is assumed to be concentrated.

K is called the Radius of Gyration of the body about the axis of rotation. It is equal to the root mean square distance of all particles from the axis of rotation of the body.

16. What are the theorems on moment of inertia?

There are two important theorems which help to find the moment of inertia of a body about some other axis if moment of inertia about any symmetrical axis of the body is given. These are called theorem of parallel and perpendicular axes.

They are

1. Parallel axes theorem and

2. Perpendicular axes theorem

17. State parallel axis theorem.

The moment of inertia of a body about any axis is equal to the sum of its moment of inertia about a parallel axis passing through its centre of gravity of the body and the product of its mass of the body with the square of the distance between the two axes.

18. State perpendicular axis theorem.

It states that the moment of inertia of a plane lamina about an axis perpendicular to its plane is equal to the sum of the moments of inertia of the plane lamina about any two mutually perpendicular axes in its own plane and intersecting each other at the point where the perpendicular axis passes through it.

19. Define angular momentum.

Angular momentum of a particle is defined as its moment of linear momentum it is given by the product of linear momentum and perpendicular distance of its line of action from the axis of rotation. It is denoted by

20. Define torque.

The moment of the applied force is called torque. It is represented by the symbol ‘τ’.

If F is the force acting on a body at a distance r then,

Torque = Force × distance

The rotational motion is due to only when the torque acts on the body.

21. State conversation of angular momentum.

The law of conservation of angular momentum states that in the absence of an external torque, the angular momentum of a body or a system of bodies remains conserved.

22. What is gyroscope?

A gyroscope is a device used for measuring or maintaining orientation and angular velocity. It is a spinning wheel or disc in which the axis of rotation (spin axis) is free to assume any orientation by itself.

23. What are the uses of gyroscope?

1. In view of the property of stability, the gyroscope are used as stabilizers in ships, boats and aeroplanes.

2. Due to the inherent stability of the gyroscope, it is used as a compass, and a gyro-compass is preferable to the magnetic compass in many respects.

3. Another important application of the directional stability of a rapidly spinning (rotating) body is the rifling of the barrels of the rifles.

24. What is torsional pendulum?

A circular metallic disc suspended using a thin wire that executes torsional oscillation is called torsional pendulum.

25. What are the uses of torsional pendulum?

Torsional pendulum is used to determine

1. Rigidity modulus of the wire

2. Moment of inertia of the disc

3. Moment of inertia of an irregular body.

26. What is double pendulum?

A double pendulum is a pendulum with another pendulum attached to its end.

The pendulum behaves like a linear system for small angles. When the angles are small in the double pendulum, the system behaves like the linear double spring. In this case, the motion is determined by simple sine and cosine functions.

On the otherhand for large angles, the pendulum is non-linear and the phase graph becomes much more complex.