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
(a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be , where M is the mass of the sphere and R is the radius of the sphere.
(b) Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be , find its moment of inertia about an axis normal to the disc and passing through a point on its edge.
(b) Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be , find its moment of inertia about an axis normal to the disc and passing through a point on its edge.
Q2
Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time?
Q3
A solid cylinder of mass 20 kg rotates about its axis with angular speed . The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?
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Chapter 8: Gravitation
33 questions
Question
Medium
Solving time: 2 mins
Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time?
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Text solution
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The moment of inertia for the hollow cylinder=
The moment of inertia for the solid sphere=
For hollow sphere we have
For solid sphere we have
Thus
The angular velocity() at a certain time will be greater for solid sphere.
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Practice more questions from Physics Part-I (NCERT)
Q1
(a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be , where M is the mass of the sphere and R is the radius of the sphere.
(b) Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be , find its moment of inertia about an axis normal to the disc and passing through a point on its edge.
(b) Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be , find its moment of inertia about an axis normal to the disc and passing through a point on its edge.
Q2
Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time?
Q3
A solid cylinder of mass 20 kg rotates about its axis with angular speed . The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?
View allPractice questions from Physics Part-I (NCERT)
Question 1
Easy
Views: 5,439
(a) Give the direction of frictional force at B, and the sense of frictional torque, before perfect rolling begins.
(b) What is the force of friction after perfect rolling begins ?
Question 2
Hard
Views: 6,246
(a) Compute the angular acceleration of the wheel.
(b) Find the work done by the pull, when 2m of the cord is unwound.
(c) Find also the kinetic energy of the wheel at this point. Assume that the wheel starts from rest.
(d) Compare answers to parts (b) and (c).
Question 3
Medium
Views: 6,271
Question 4
Medium
Views: 5,786
(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.)
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| Question Text | Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time? |
| Updated On | Nov 30, 2022 |
| Topic | System of Particles and Rotational Motion |
| Subject | Physics |
| Class | Class 11 |
| Answer Type | Text solution:1 Video solution: 3 |
| Upvotes | 305 |
| Avg. Video Duration | 4 min |
