It is important for the students that all the concepts should be very clear for better marks in future. Here, we are providing important conceptual questions and answers for class 11 physics chapter 7 System of particles and Rotational Motion. In this lesson, students will learn about System of particles and Rotational Motion. This will not only help the students to know the important questions but will also help them during revision.
Q.1. What is centre of mass of a system of particles?
Ans. The point in the system, where the whole mass of the system can be supposed to be concentrated, is called centre of mass of the system.
Q.2. Where does the centre of mass of a two particle
system lie, if one particle is more massive than the
Ans. The centre of mass of the two particle system lie nearer to the massive of the two particles.
Q.3. Is centre of mass a reality?
Ans. No. It is only a mathematical concept.
Q.4. Should there exist mass at the location of centre
of mass of a system?
Ans. There is nothing at the location of the centre of mass. It is just a useful mathematical concept to simplify the study of the motion of rigid body.
Q.5. What will be nature of motion of centre of mass
of an isolated system?
Ans. The centre of mass of an isolated system (no external force acting on the system) will either be at rest or it must be moving with a constant velocity.
Q.6. Where does the centre of mass of a rectangle lie?
Ans. At the point of intersection of the diagonals of the rectangle.
Q.7. What is the location of centre of mass of a
Ans. At the centroid of the triangle i.e. at the point, where the medians of the triangle meet.
Q.8. Should the centre of mass of a body necessarily
lie inside the body?
Ans. Not necessarily. For example, the centre of mass of a ring lies at the centre of the ring i.e. at a point, where actually there is no mass.
Q.9. Give one example each for a body, where the
centre of mass lies inside the body and outside the
Ans. The centre of mass of a solid or a hollow sphere lies at its centre. However, in case of a solid sphere, the centre of mass lies inside the body; where as in case of a hollow sphere, it lies outside the body.
Q.10. What will be the position of the centre of mass of two particles of equal masses, moving opposite to each other with the same velocity? Ans. If the two particles of equal masses are moving opposite to each other with the same velocity, the centre of mass will always lie at the centre of the line joining the position of the two particles.
Q.11. Is it necessary that centre of mass should always
lie inside the body?
Ans. No, it is not necessary that centre of mass should always lie inside the body. For example in case of a ring, the centre of mass is at the centre of the ring and thus, it lies outside the body.
Q.12. What is the position of centre of mass in case of
a (i) uniform rod, (ii) cylindrical body, (iii) conical
body, (iv) circular ring?
- (i) At the middle point of the rod.
- (ii) At the middle point of the axis of the cylindrical body.
- (iii) On the line joining the apex to the centre of the base at a distance equal to 1/4th of the length of this line from the base.
- (iv) At the centre of the circular ring.
Q.13. How is it possible to describe the motion of a big
system, when Newton's law of motion are applicable
to individual particles of the system? Explain.
Ans. The motion of a big system under the effect of external forces on the constituent particles can be studied by writing the separate equations of motion for the constituting particles. Obviously, it will offer a lot of difficulty. Because of this reason, the motion of a big system is studied by writing equation of motion for the centre of mass of the system, when all the external forces acting on the system are applied directly on the centre of mass.
Q.14. What is the difference between centre of gravity
and centre of mass?
Ans. The centre of gravity of a body is a point, where the whole weight of the body can be supposed to act. Further, the total gravitational torque on the body about its centre of gravity is always zero. The centre of mass of a body is a point, where the whole mass of the body can be supposed to be concentrated. In fact, nothing exists at the location of the centre of mass. It is only a mathematical concept. The motion of the body under the action of external forces can be studied by studying the motion of centre of mass, then all the external forces are applied directly on it. The centre of mass and centre of gravity are two different concepts. However, the centre of gravity of the body coincides with the centre of mass in uniform gravity or gravity-free area.
Q.15. A body A of mass M, while falling vertically
downwards under gravity, breaks into two parts: a
body B of mass M/3 and a body of mass 2M/3. How
does the centre of mass of bodies B and C taken
together shift compared to that of body A?
Ans. The centre of mass of the two parts B and C of the body will not shift. It is because, after breaking into two parts no external force acts on the system. It still moves under the effect of gravity. Hence, the centre of mass of the two parts B and C will follow the original path.
Q.16. A rocket is out in free space shooting out a
stream of exhaust gases and picking up speed in the
opposite direction. What happens to the centre of
mass of all the matter, that which is ejected and that
which is left in the rocket?
Ans. A rocket moving in the free space represents an isolated system, consisting of the ejected matter and that which is left in the rocket. Since no external force is acting on the rocket system, the acceleration of its centre of mass must be zero. In other words, the velocity of the centre of mass of all the matter (matter ejected + matter left) remains constant.
Q.17. What is the condition for two vectors to be
parallel to each other?
Ans. The two vectors are parallel to each other if their cross product is zero.
Q.18. Do the internal forces affect the motion of a
system under the effect of some external force?
Ans. No. Torque acting on the system due to internal forces cancel out.
Q.19. What do you mean by a rigid body?
Ans. A body whose constituent particles remain at their respective positions, when a body is in translational or rotational motion is called a rigid body.
Q.20. What is meant by torque in rotational motion?
Ans. The turning effect of a force about the axis of rotation is called torque of the force and it is measured as the product of the magnitude of the force and the perpendicular distance of the line of action of the force from the axis of rotation.
Q.21. Give the SI unit of torque and write its
Ans. The SI unit of torque is Newton metre (N-m). The dimensional formula of torque is [ML2T-2].
Q.22. Define angular momentum. Give its SI unit.
Ans. The turning moment of a particle about the axis of rotation is called the angular momentum of the particle and is measured as the product of the linear momentum and the perpendicular distance of its line of action from the axis of rotation. It is denoted by L.
The SI unit of angular momentum is kg m2s-1.
Q.23. Write the dimensional formula of angular
Ans. The dimensional formula of angular momentum is [ML2T-1].
Q.24. Can a torque be balanced by a single force?
Ans. A torque produces rotational motion, where as a single force can produce translational motion. Since their effects are entirely different, a torque cannot be balanced by a single force.
Q.25. State the law of conservation of angular
Ans. The law of conservation of angular momentum states that if no external torque acts on a system, then the total angular momentum of the system always remains conserved.
Q.26. Explain, why it is difficult to open a door by
pushing or pulling it near the hinge.
Ans. To open a door, torque has to be applied. Since
torque = force × moment arm
the torque is lesser, when force is applied on the door near the hinges. As a result, it proves difficult to open the door.
Q.27. Torque and work are both defined as force
times distance. Explain, how do the differ?
Ans. (i) Whereas work is a scalar quantity, torque is a vector quantity. (ii) Work done is measured as the product of the applied force and the distance, which the body covers along the direction of the force. On the other hand, torque is measured as the product of the force and its perpendicular distance from the axis of rotation.
Q.28. Why is a ladder more apt to slip, when you are
high up on it than when you just begin to climb?
Ans. When a person is high up on a ladder, then torque produced due to his weight about the point of contact between the ladder and the floor becomes quite large. On the other hand, when he starts climbing up the torque is small. Due to this reason, the ladder is more apt to slip, when one is high up on it.
Q.29. A projectile acquires angular momentum about
its point of projection during its flight. Is its angular
momentum constant over the entire orbit?
Ans. An object will not acquire angular momentum if no external torque acts on it. During its flight, a torque acts on the projectile due to gravity and hence it acquires angular momentum.
Q.30. A planet revolves around a massive star in a
highly elliptical orbit. Is its angular momentum
constant over the entire orbit?
Ans. The planet moves around the star under the effect of the gravitational force, which is purely radial in nature. Since for a body moving under the effect of radial force, the angular momentum is independent of the nature of trajectory, the angular momentum of the planet will remain constant.
Q.31. State principle of moments.
Ans. The principle of moments states that if a body is in rotational equilibrium under the action of a number of forces, then the sum of clockwise moments is equal to the sum of anti-clockwise moments.
Q.32. Define couple.
Ans. A couple is defined as the pair of two equal and unlike parallel forces acting on a rigid body along different lines of action. The turning effect of a couple is called moment of couple or torque exerted by the couple.
Q.33. Give a few examples of the application of couple
from our daily life.
Ans. Following are a few examples of the application of couple from our daily life:-
- (i) To open or close a water tap, a couple is applied with the help of fingers and thumb of ourhand.
- (ii) Again to open the lid of a bottle, a couple is applied with the help of fingers and thumb of our hand.
- (iii) The earth's magnetic field exerts equal and opposite forces on the poles of a compass needle. These two forces constitute a couple.
Q.34. What are the properties of couple?
Ans. Following are a few important properties of a couple:-
- (i) A couple always produces a rotational motion. A couple acting on a rigid body accelerates or retards the rotational motion of the body. In other words, when a couple acts on a body it produces angular acceleration in the motion of the body.
- (ii) The moment of couple is a vector quantity.
- (iii) The moment of couple about any point in its plane is always constant. (iv) A couple can only be balanced by an equal and opposite couple. A couple cannot be balanced by a single force.
- (v) A couple can be shifted as such without affecting its moment.
- (vi) If a body is under the action of a number of external forces, then in general their effect is equivalent to a resultant force plus a couple.
Q.35. Define moment of inertia.
Ans. The moment of inertia of a rigid body about a given axis of rotation is the sum of the products of the masses of the various particles and squares of their perpendicular distances from the axis of rotation.
Q.36. Is there any difference between moment of
inertia and rotational inertia?
Ans. The moment of inertia is another name for rotational inertia.
The moment of inertia is called rotational inertia for the reason that it gives the measure of inertia of a body during its rotational motion.
Q.37. Is moment of inertia a scalar or vector quantity?
Ans. Moment of inertia is a scalar quantity.
Q.38. Does moment of inertia change with change of
the axis of rotation?
Ans. Yes, the moment of inertia changes with change of the axis of rotation.
Q.39. Does moment of inertia of a rigid body change
with change with the speed of rotation?
Ans. No, the moment of inertia of a rigid body does not change with change with the speed of rotation.
Q.40. What are the factors on which the moment of
inertia of a body depend?
(1) Mass of the body.
(2) Distribution of mass about the axis of rotation.
Q.41. Give the physical significance of moment of
Ans. The moment of inertia of a body place the same role in rotational motion as its mass does in linear motion.
Q.42. Define radius of gyration.
Ans. It is defined as the distance from the axis of rotation at which, if whole mass of the body were supposed to be concentrated, the moment of inertia would be same as with the actual distribution of the mass of body in the form of the constituting particles.
Q.43. Is radius of gyration of a body constant
Ans. No, It changes with the change in the position of the axis of rotation.
Q.44. Which physical quantities are represented by
(a) Product of moment of inertia and angular velocity.
(b) Product of moment of inertia and angular
(a) Angular momentum
Q.45. State the theorem of parallel axes.
Ans. Theorem of parallel axis:- 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 lamina about any two mutually perpendicular axes in its plane and intersecting each other at the point, where the perpendicular axis passes through it.
Q.46. State the theorem of perpendicular axes.
Ans. Theorem of perpendicular axes:- It states that the moment of inertia of a rigid body about any axis is equal to its moment of inertia about a parallel axis through its centre of mass plus the product of the mass of the body and the square of the perpendicular distance between the two axes.
Q.47. In a fly wheel, most of the mass is concentrated
at the rim Explain, Why?
Ans. In a fly wheel, most on the mass is concentrated at the rim. Due to this peculiar shape, the fly wheel possesses a large value of moment of inertia for the given mass and the radius.
If such a wheel gains or loses some rotational energy, it brings about only a very small change in its angular speed. In this way, a fly wheel helps to maintain uniform motion.
Q.48. Will two spheres of equal mass one solid and
the other hollow have equal moment of inertia?
Ans. Though the masses of two spheres are equal, the M.I. of the solid and the hollow spheres will not be equal. The M.I. of the hollow sphere will be more than that of the solid sphere. It is because, the mass is distributed at large distances from the axis of rotation in case of a hollow sphere.
Q.49. How will you distinguish between a hard boiled
egg and a raw egg by spinning each on a table top?
Ans. The egg which spins faster will be the hard boiled egg. It is because, a hard boiled will spin (rotate) more or less as a rigid body, where a raw egg will not do so. In case of a raw egg, its matter in the liquid state moves away from the axis of rotation, thereby increasing the moment of inertia. As M.I. of the raw egg is more, the acceleration produced will be lesser, when the same torque is applied in both the cases to set them spinning.
Q.50. The angular velocity of revolution of the earth
around the sun increases, when it comes closer to the
Ans. The Earth revolves around the sun in elliptical orbit with the sun at one of the two focii of the elliptical orbit. Therefore, moment of inertia of the earth about an axis through the sun keeps on changing due to change in its distance from the sun. Since no external torque acts on the earth, its angular momentum must remain conserved. In order it remains so, the angular velocity of earth increases when the moment of inertia of earth decreases and vice versa.
Q.51. How does an ice-skater, a ballet dancer or an
acrobat take advantage of the principle of
conservation of angular momentum?
Ans. An ice skater, a ballet dancer or an acrobat is able to change his angular speed during the course of his performance. When the performer stretches out his hands and legs, his moment of inertia increases and the angular speed decreases. On the other hand, when he folds his hands and legs near his body, the moment of inertia decreases and he is able to increase his angular speed.