physics ncert solutions class 11th

14.4 Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic and (c) non-periodic motion? Give period for each case of periodic motion ( $\mathit{\omega }$ is any positive constant):

(a) Sin $\mathit{\omega }$ t – cos $\mathit{\omega }$ t

(b) Sin³ $\mathit{\omega }$ t

(c) 3 cos ( $\mathit{\pi }$ /4 – 2 $\mathit{\omega }$ t)

(d) Cos $\mathit{\omega }$ t + cos 3 $\mathit{}\mathit{\omega }$ t + cos 5 $\mathit{}\mathit{\omega }$ t

(e) Exp (– $\mathit{\omega }$ 2t2)

(f) 1 + $\mathit{\omega }$ t + $\mathit{\omega }$ ²t²

14.3 Fig. 14.23 depicts four x-t plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion)?

14.2 Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?

(a) The rotation of earth about its axis.

(b) Motion of an oscillating mercury column in a U-tube.

(c) Motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower most point.

(d) General vibrations of a polyatomic molecule about its equilibrium position.

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

6.30 Consider the decay of a free neutron at rest : n $\to$ p + e .Show that the two-body decay of this type must necessarily give an electron of fixed energy and, therefore, cannot account for the observed continuous energy distribution in the $\mathit{\beta }$ -decay of a neutron or a nucleus (Fig. 6.19).

6.29 Which of the following potential energy curves in Fig. 6.18 cannot possibly describe the elastic collision of two billiard balls ? Here r is the distance between centers of the balls.