- Chapter 1- Physical World
- Chapter 2- Units and Measurements
- Chapter 3- Motion in a Straight Line
- Chapter 4- Motion in a plane
- Chapter 5- Laws of motion
- Chapter 6- Work Energy and power
- Chapter 8- Gravitation
- Chapter 9- Mechanical Properties Of Solids
- Chapter 10- Mechanical Properties Of Fluids
- Chapter 11- Thermal Properties of matter
- Chapter 12- Thermodynamics
- Chapter 13- Kinetic Theory
- Chapter 14- Oscillations
- Chapter 15- Waves

Chapter 1- Physical World |
Chapter 2- Units and Measurements |
Chapter 3- Motion in a Straight Line |
Chapter 4- Motion in a plane |
Chapter 5- Laws of motion |
Chapter 6- Work Energy and power |
Chapter 8- Gravitation |
Chapter 9- Mechanical Properties Of Solids |
Chapter 10- Mechanical Properties Of Fluids |
Chapter 11- Thermal Properties of matter |
Chapter 12- Thermodynamics |
Chapter 13- Kinetic Theory |
Chapter 14- Oscillations |
Chapter 15- Waves |

.Give the location of the center of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does not the center of mass of a body necessarily lie inside the body ?

**Answer
1** :

A sphere. Center of the sphere

A ring. Center of the ring

A cylinder. Middle point on the axis of the cylinder

A cone. At a point distant 1/4^{th} of height of the cone from the base on the axis of the cone.

A cube. Point of intersection of diagonals.

No, center of mass of a ring and bangle lies inside the hollow portions of the ring and bangle.

**Answer
2** :

Let us choose the nucleus of the hydrogen atom as theorigin for measuring distance.

Mass of hydrogen atom, m_{1} =1 unit (say)

Mass of chlorine atom, m_{2} =35.5 units (say)

Now, x_{1}= 0 and x_{2} = 1.27 A

= 1.27 x 10^{-10} m

Distance of C.M. of HCl molecule from the origin isgiven by

Mass of hydrogen atom, m

Mass of chlorine atom, m

Now, x

= 1.27 x 10

Distance of C.M. of HCl molecule from the origin isgiven by

**Answer
3** :

Trolley and the child makes the system. Speed of the C.M. ofthis system remains same irrespective of the movements of the child inside thetrolley in any manner because C.M. is affected by external forces and not bythe internal forces.

of a x b.

**Answer
4** :

**Answer
5** :

Let a parallelepiped be formed on the three vectors

**Answer
6** :

**Answer
7** :

Let at a certain instant twoparticles be at points P andQ, as shown in the following figure.

Angular momentum of the system about point P:

Angular momentum of the system about point Q:

Consider a point R, which is at a distance *y* from point Q, i.e.,

QR = *y*

∴PR = *d – y*

Angular momentum of the system about point R:

Comparing equations (*i*), (*ii*),and (*iii*), we get:

We infer from equation (*iv*) that the angular momentum of a system does notdepend on the point about which it is taken.

**Answer
8** :

As is clear form Fig.,

θ_{1} = 36.9°,θ_{2} = 53.1°.

If T_{1} ,T_{2} are the tensions inthe two strings, then for equilibrium along the horizontal,

T_{1} sin θt = T_{2} sin θ_{2}

θ

If T

T

**Answer
9** :

Here, m = 1800 kg

Distance of center of gravity (C) behind the front axle = 1.05 m.

Let R_{1}. R_{2} be the force exertedby the level ground on front wheels and back wheels. As is clear from fig.,

R_{1}+ R_{2} = mg = 1800 x 9.8 =17640 N

For rotational equilibrium about C,

Distance of center of gravity (C) behind the front axle = 1.05 m.

Let R

R

For rotational equilibrium about C,

(b) What is the moment of inertia of a uniform disc of radius R and mass Mabout an axis

(1) passing through its center and normal to the disc

(2) passing through a point on its edge and normal to the disc ? The moment ofinertia of the disc about any of its diameters is given to be

**Answer
10** :

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