CBSE Class 12 Physics Centre of Mass Assignment

CBSE Class 12 Physics Centre of Mass Assignment. Please refer to the examination notes which you can use for preparing and revising for exams. These notes will help you to revise the concepts quickly and get good marks.

Centre of mass assignment for CBSE Class 12 Physics with a comprehension passage on collisions, followed by multiple choice questions and assertion-reason questions on centre of mass, elastic and inelastic collisions, and centre of gravity, with answers and teacher's notes.

MISCELLANEOUS ASSIGNMENT

Comprehension-1

In physics we can across many examples of collisions. The molecules of a gas collide with one another and with the centainer. The collision of a neutron with an atom is well known. In a nuclear reactor fast neutrons produced in the fission of uranium atom have to be slowed down. They are, therefore, made to collide with hydrogen atoms. The term collision does not necessarily mean that a particle or a body must actually strike another. In fact, two particles may not even touch each other and yet they are said to collide if one particle influences the motion of the other. When two bodies collide, each body exerts an equal and opposite force on the other. The fundamental conservation law of physics are used to determine the velocities of the bodies after the collision. Collision may be elastic or inelastic. Thus a collision may be defined as an event in which two or more bodies exert relatively strong forces on each other for a relatively short time. The forces that the bodies exert on each other are internal to the system.

Almost all the knowledge about the sub-atomic particles such as electrons, protons, neutrons, muons, quarks, etc. is obtained from the experiments involving collisions.

There are certain collisions called nuclear reactions in which new particles are formed. For example, when a slow neutron collides with a uranium-235 nucleus, new nuclei baruim-141 and krypton-92 are formed. This collision is called nuclear fission. In nuclear fusion, tow nuclei deuterium and trituim collide (or fuse) to form a helium nucleus with the emission of a neutron.

1. Which one of the following collisions is not elastic?
(a) A hard steel ball dropped on a hard concrete floor and rebounding to its original height.
(b) Two balls moving in the same direction collide and strick to each other
(c) Collision between molecules of an ideal gas
(d) Collisions of fast neutrons with hydrogen atoms in a fission reactor.

Answer: (b) Two balls moving in the same direction collide and strick to each other

1. An elastic collision conserves total kinetic energy.
2. In option (a), the ball rebounds to its original height, so no kinetic energy is lost; this is elastic.
3. Options (c) and (d) are also elastic, since molecular collisions and neutron-hydrogen collisions conserve kinetic energy.
4. In option (b), the two balls stick together after collision, so kinetic energy is lost and the collision is not elastic.
5. Hence, the correct option is (b).

Teacher's Note:
a) An elastic collision conserves both kinetic energy and momentum.
b) Bodies that stick together after impact form a perfectly inelastic collision.
c) A ball rebounding to its original height is a sign that no energy was lost.

2. Which one of the following statements is true about inelastic collisions?
(a) The total kinetic energy of the particles after collision is equal to that before collision
(b) The total kinetic energy of the particles after collision is less than that before collision.
(c) The total momentum of the particles after collision is less than that before collision.
(d) Kinetic energy and momentum are both conserved in the collision.

Answer: (b) The total kinetic energy of the particles after collision is less than that before collision.

1. In an inelastic collision, some kinetic energy is converted into heat, sound or deformation.
2. So the kinetic energy after collision is less than before collision.
3. Momentum is always conserved in collisions, so option (c) is wrong.
4. Option (d) is wrong because kinetic energy is not conserved in an inelastic collision.
5. Hence, the correct option is (b).

Teacher's Note:
a) Momentum is conserved in every collision, elastic or inelastic.
b) Only kinetic energy is lost in an inelastic collision.
c) Watch for options that say "momentum less than before", since they are a common trap.

3. In elastic collisions
(a) only energy is conserved
(b) only momentum is conserved
(c) neither energy nor momentum is conserved
(d) both energy and momentum are conserved.

Answer: (d) both energy and momentum are conserved.

1. In an elastic collision, the total kinetic energy before and after collision is the same.
2. The total momentum of the colliding bodies is also conserved in every collision.
3. Hence, both energy and momentum are conserved, and the correct option is (d).

Teacher's Note:
a) Elastic means kinetic energy is conserved in addition to momentum.
b) Option (b) fails because energy is also conserved in an elastic collision.

Each of the questions given below consists of two statements, an assertion (A) and reason (R).
Select the number corresponding to the appropriate alternative as follows
(a) If both A and R are true and R is the correct explanation of A
(b) If both A and R are true but R is not the correct explanation of A
(c) If A is true but R is false
(d) If A is false but R is true

4. A. When two bodies of different masses are just released from different positions above the ground, then acceleration of their centre of mass is zero.
R. When bodies move, their centre may change position but is not accelerated.
(a) If both A and R are true and R is the correct explanation of A
(b) If both A and R are true but R is not the correct explanation of A
(c) If A is true but R is false
(d) If A is false but R is true

Answer: (d) If A is false but R is true

1. Both bodies fall freely under gravity, so each has acceleration g downward.
2. The acceleration of the centre of mass is therefore g, not zero, so A is false.
3. A body in free fall is accelerated, so the statement in R is also false.
4. Option (d) is the only option in which A is false, so it is retained as printed in the key.

Teacher's Note:
a) Free-falling bodies accelerate at g, and so does their centre of mass.
b) The centre of mass of a system moves only if an external force acts on it; here gravity acts on both bodies.
c) Both statements are false in this question, so read the options carefully before choosing.

5. A. The centre of mass of a proton and an electron, released from their respective positions remains at rest.
R. The proton and electron attract and move towards each other. No external force is applied, therefore, their centre of mass remains at rest.
(a) If both A and R are true and R is the correct explanation of A
(b) If both A and R are true but R is not the correct explanation of A
(c) If A is true but R is false
(d) If A is false but R is true

Answer: (a) If both A and R are true and R is the correct explanation of A

1. No external force acts on the proton-electron system.
2. With zero external force, the acceleration of the centre of mass is zero.
3. The particles move towards each other, but their internal forces do not move the centre of mass.
4. Hence, both A and R are true, and R explains A.

Teacher's Note:
a) Internal forces cannot change the motion of the centre of mass.
b) The two particles move towards a common point that stays fixed.

6. A. The centre of mass of a body may lie where there is no mass.
R. Centre of mass of a body is a point, where the whole mass of the body is supposed to be concentrated.
(a) If both A and R are true and R is the correct explanation of A
(b) If both A and R are true but R is not the correct explanation of A
(c) If A is true but R is false
(d) If A is false but R is true

Answer: (b) If both A and R are true but R is not the correct explanation of A

1. The centre of a ring lies at its geometric centre, where there is no mass, so A is true.
2. R is a correct definition of centre of mass.
3. The definition does not explain why the centre of mass can lie outside the body, so R is not the explanation of A.
4. Hence, the correct option is (b).

Teacher's Note:
a) A ring or a hollow sphere is a good example of a centre of mass lying in empty space.
b) A true definition does not always explain a related fact.

7. A. When a body dropped from a height explodes in mid air, the pieces fly in such a way that their centre of mass keeps moving vertically downwards.
R. Explosion occurs under internal forces only. External force = 0.
(a) If both A and R are true and R is the correct explanation of A
(b) If both A and R are true but R is not the correct explanation of A
(c) If A is true but R is false
(d) If A is false but R is true

Answer: (a) If both A and R are true and R is the correct explanation of A

1. The explosion forces are internal, so they do not change the motion of the centre of mass.
2. The body was moving vertically downwards before the explosion, so its centre of mass keeps moving vertically downwards.
3. The explosion takes a very short time, so the impulse of gravity during it is negligible and the external force is taken as zero.
4. Hence, both A and R are true, and R explains A.

Teacher's Note:
a) Internal forces never change the velocity of the centre of mass.
b) Gravity still acts during the explosion, but its effect over a very short time is negligible.

8. A. The centre of mass of a circular disc lies always at the centre of the disc.
R. Circular disc is a symmetrical body.
(a) If both A and R are true and R is the correct explanation of A
(b) If both A and R are true but R is not the correct explanation of A
(c) If A is true but R is false
(d) If A is false but R is true

Answer: (d) If A is false but R is true

1. The centre of mass of a circular disc lies at its centre only when the mass is uniformly distributed.
2. The word "always" makes A false, because a disc with uneven density has its centre of mass elsewhere.
3. A circular disc is a symmetrical body, so R is true.
4. Hence, the correct option is (d).

Teacher's Note:
a) Symmetry places the centre of mass at the centre only for a uniform body.
b) Words such as "always" in an assertion often make it false.

9. A. At the centre of earth, a body has centre of mass, but no centre of gravity.
R. This is because g = 0 at the centre of earth.
(a) If both A and R are true and R is the correct explanation of A
(b) If both A and R are true but R is not the correct explanation of A
(c) If A is true but R is false
(d) If A is false but R is true

Answer: (a) If both A and R are true and R is the correct explanation of A

1. The centre of mass depends only on the distribution of mass, so it exists at the centre of the earth.
2. The centre of gravity is the point where the weight of the body acts; weight equals mass times g.
3. At the centre of the earth, g = 0, so the weight and its point of action are not defined.
4. Hence, both A and R are true, and R explains A.

Teacher's Note:
a) Centre of mass does not depend on g, but centre of gravity does.
b) A body with zero weight has no centre of gravity.

10. A. The centre of mass of a body may lie where there is no mass.
R. The centre of mass has nothing to do with the mass.
(a) If both A and R are true and R is the correct explanation of A
(b) If both A and R are true but R is not the correct explanation of A
(c) If A is true but R is false
(d) If A is false but R is true

Answer: (c) If A is true but R is false

1. A is true, since the centre of mass of a ring lies in the empty space at its centre.
2. R is false, because the position of the centre of mass depends on how the mass is distributed.
3. Hence, the correct option is (c).

Teacher's Note:
a) The centre of mass is found from the mass and its distribution, so R cannot be true.
b) The printed key shows (b); the correct answer is (c) because the reason is false.