Physics Part-I
Class 11
NCERT
1
Chapter 1: Physical World
16 questions
2
Chapter 2: Units and Measurements
51 questions
3
Chapter 3: Motion in Straight Line
50 questions
4
Chapter 4: Motion in a Plane
43 questions
5
Chapter 5: Laws of motion
52 questions
6
Chapter 6: Work, Energy and Power
41 questions
7
Chapter 7: System of Particles and Rotational Motion
45 questions
Q1
Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie inside the body ?
Q2
In the HCl molecule, the separation between the nuclei of the two atoms is about . Find the approximate location of the CM of the molecule, given that a chlorine atom is about 35.5 times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus.
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Chapter 8: Gravitation
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Question
Medium
Solving time: 1 mins
Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie inside the body ?
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In all the four cases, as the mass density is uniform, centre of mass is located at their respective geometrical centres.
i) Sphere - Centre of Sphere
ii) Cylinder - Middle Point on axis of cylinder
iii) Ring - At centre of ring (Outside the ring)
iv) Cube - At point of intersection of diagnols
No, it is not necessary that the centre of mass of a body should lie on the body. For example, in case of a circular ring, centre of mass is at the centre of the ring, where there is no mass.
No, it is not necessary that the centre of mass of a body should lie on the body. For example, in case of a circular ring, centre of mass is at the centre of the ring, where there is no mass.
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Practice more questions from Physics Part-I (NCERT)
Q1
Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie inside the body ?
Q2
In the HCl molecule, the separation between the nuclei of the two atoms is about . Find the approximate location of the CM of the molecule, given that a chlorine atom is about 35.5 times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus.
View allPractice questions from Physics Part-I (NCERT)
Question 1
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Question 2
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(a) Show
where is the momentum of the th particle (of mass ) and . Note is the velocity of the th particle relative to the centre of mass.
Also, prove using the definition of the center of mass
(b) Show
where is the total kinetic energy of the system of particles, is the total kinetic energy of the system when the particle velocities are taken with respect to the centre of mass and is the kinetic energy of the translation of the system as a whole (i.e. of the centre of mass motion of the system). The result has been used in Sec. 7.14.
(c) Show
where is the angular momentum of the system about the centre of mass with velocities taken relative to the centre of mass. Remember ; rest of the notation is the standard notation used in the chapter. Note and can be said to be angular momenta, respectively, about and of the centre of mass of the system of particles.
(d) Show
Further, show that
where is the sum of all external torques acting on the system about the centre of mass.
(Hint : Use the definition of centre of mass and Newtons Third Law. Assume the internal forces between any two particles act along the line joining the particles.)
Question 3
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Question 4
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(b) Is kinetic energy conserved in the process? If not, from where does the change come about?
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| Question Text | Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie inside the body ? |
| Updated On | Nov 3, 2022 |
| Topic | System of Particles and Rotational Motion |
| Subject | Physics |
| Class | Class 11 |
| Answer Type | Text solution:1 Video solution: 2 |
| Upvotes | 253 |
| Avg. Video Duration | 10 min |
