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# NCERT Solutions for Class 11 Physics Chapter 7 System of particles and Rotational Motion

## NCERT Solutions for Class 11 Physics Chapter 7 System of particles and Rotational Motion

NCERT Solutions for Class 11 Physics Chapter 7 System of particles and Rotational Motion is designed and prepared by the best teachers across India. All the important topics are covered in the exercises and each answer comes with a detailed explanation to help students understand concepts better. These NCERT solutions play a crucial role in your preparation for all exams conducted by the CBSE, including the JEE.

### NCERT TEXTBOOK QUESTIONS SOLVED

**1. 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?**

**Ans.** In all the four cases, as the mass density is uniform, centre of mass is located at their respective geometrical centres.

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.

**2. A child sits stationary at one end of a long trolley moving uniformly with a speed V on a smooth horizontal floor. If the child gets up and runs about on the trolley in any manner, what is the speed of the CM of the (trolley + child) system?**

**Ans.** When the child gets up and runs about on the trolley, the speed of the centre of mass of the trolley and child remains unchanged irrespective of the manner of motion of child. It is because here child and trolley constitute one single system and forces involved are purely internal forces. As there is no external force, there is no change in momentum of the system and velocity remains unchanged.

**3. (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 2 MR2/5, 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 1 be 1/4 MR2, find the moment of inertia about an axis normal to the disc 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 1 be 1/4 MR2, find the moment of inertia about an axis normal to the disc passing through a point on its edge.

**Ans.** (a) Moment of inertia of sphere about any diameter = 2/5 MR2

Applying theorem of parallel axes,Moment of inertia of sphere about a tangent to the sphere = 2/5 MR2 +M(R)2 =7/5 MR2

(b) We are given, moment of inertia of the disc about any of its diameters = 1/4 MR2

(i) Using theorem of perpendicular axes, moment of inertia of the disc about an axis passing through its centre and normal to the disc = 2 x 1/4 MR2 = 1/2 MR2.

(ii) Using theorem axes, moment of inertia of the disc passing through a point on its edge and normal to the dies = 1/2 MR2+ MR2 = 3/2 MR2.

**4. 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?**

**Ans.** Let M be the mass and R the radius of the hollow cylinder, and also of the solid sphere. Their moments of inertia about the respective axes are I1 = MR2 and I2 = 2/5 MR2

Let Ï„ be the magnitude of the torque applied to the cylinder and the sphere, producing angular accelerations Î±1and Î±2 respectively. Then Ï„=I1 Î±1 = I2 Î±2

The angular acceleration 04 produced in the sphere is larger. Hence, the sphere will acquire larger angular speed after a given time.

**5. A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s-1. 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?**

**Ans.** M = 20 kg

Angular speed, w = 100 rad s-1; R = 0.25 m

Moment of inertia of the cylinder about its axis

=1/2 MR2 = 1/2 x 20 (0.25)2 kg m2 = 0.625 kg m2

Rotational kinetic energy,

Er = 1/2 Iw2 = 1/2 x 0.625 x (100)2 J = 3125 J

Angular momentum,

L = Iw = 0.625 x 100 Js= 62.5 Js.