Physics

14.1 Which of the following examples represent periodic motion?

(a) A swimmer completing one (return) trip from one bank of a river to the other and back

(b) A freely suspended bar magnet displaced from its N-S direction and released

(c) A hydrogen molecule rotating about its centre of mass

(d) An arrow released from a bow

We can write

$\stackrel{?}{\left|OM\right|}$ = $\left|\stackrel{?}{a}\right|\dots \dots \dots .\left(\mathrm{i}\right)$

$$ $\stackrel{?}{\left|MN\right|}$ = $\left|\stackrel{?}{b}\right|$ = $\stackrel{?}{\left|OP\right|}$ ………(ii)

$$ $\stackrel{?}{\left|ON\right|}$ = $\left|\stackrel{?}{a}+\stackrel{?}{b}\right|\dots \dots .\left(iii\right)$

In a triangle, each side is smaller than the sum of the other two sides. Therefore in ΔOMN, we have ON < (OM + MN)

$\left|\stackrel{?}{a}+\stackrel{?}{b}\right|$ < $\left|\stackrel{?}{a}\right|$ + $\left|\stackrel{?}{b}\right|$ ….(iv)

If the two vectors $\stackrel{?}{a}$ and $\stackrel{?}{b}$ act along a straight line in the same direction, then we can write $\left|\stackrel{?}{a}+\stackrel{?}{b}\right|$ = $\left|\stackrel{?}{a}\right|$ + $\left|\stackrel{?}{b}\right|\dots ..\left(v\right)$

Combining equations (iv) and (v), we get

$\left|\stackrel{?}{a}+\stackrel{?}{b}\right|$ $\le$ $\left|\stackrel{?}{a}\right|$ + $\left|\stackrel{?}{b}\right|$

Q.4.6 Establish the following vector inequalities geometrically or otherwise:

(a) |a+b| < |a| + |b|

(b) |a+b| > a| −|b

(c) |a−−b| < |a| + |b|

(d) |a−−b| > a| − |b

velocity of a freely falling body is v= $\sqrt[]{2gh}$

And $\lambda =\frac{h}{mv}=\frac{h}{m\sqrt[]{2gh}}$

$\lambda =h$ -1

 The wavelength of a photon needed to remove a proton from a nucleus which is bound to the nucleus with 1 MeV energy is nearly
a) 1.2 nm (b) 1.2 x 10-3 nm
(c) 1.2 x 10-6  nm (d). 1.2 x 10 nm

Explanation- velocity of a freely falling body is v= $\sqrt[]{2gh}$

And $\lambda =\frac{h}{mv}=\frac{h}{m\sqrt[]{2gh}}$

$\lambda =h$ -1

 The wavelength of a photon needed to remove a proton from a nucleus which is bound to the nucleus with 1 MeV energy is nearly
a) 1.2 nm (b) 1.2 x 10-3 nm
(c) 1.2 x 10-6  nm (d). 1.2 x 10 nm

What are integrated circuits (ICs), and what are their advantages?

2.35 A small sphere of radius r₁ and charge q₁ is enclosed by a spherical shell of radius r₂ and charge q₂. Show that if q₁ is positive, charge will necessarily flow from the sphere to the shell (when the two are connected by a wire) no matter what the charge q₂ on the shell is.

2.34 Describe schematically the equipotential surfaces corresponding to

(a) A constant electric field in the z-direction,

(b) A field that uniformly increases in magnitude but remains in a constant (say, z) direction,

(c) A single positive charge at the origin, and

(d) A uniform grid consisting of long equally spaced parallel charged wires in a plane.