ncert solutions physics class 11th

6.23 Power used by the family = 8 kW = 8000 W

(a) Solar energy received = 200 W/ $m^2$

Percentage conversion of Solar energy to Electrical energy = 20%

If the area required is A then 0.2 $*A*200=8000$

A = 200 $m^2$ . The comparable roof size is 14.14 X 14.14 m

4.25

Height of the aircraft from the ground = 3400m

Let A and B be the positions of the aircraft, making an angle of AOB = 30 $°$ . The perpendicular OC and OC is the height of the aircraft. Angles AOC = angle BOC = 15 $°$

In AOC, AC = OC $\tan$
$15°$ = 3400 $\tan ?15°$ = 911.03m

AB = AC + CB = 2AC = 1822m

The distance of AB is covered in 10s, so the speed of the aircraft = 1822/10 m/s = 182.2 m/s

4.24

(a) Despite being a scalar quantity, energy is not conserved in elastic collisions. False

(b) Despite being a scalar quantity, the temperature can take negative values. False

(c) The total path length is a scalar quantity. Yet it has the dimension of length. False

(d) A scalar quantity such as gravitational potential can vary from one point to another point in space. False

(e) The value of a scalar does not vary for observers with different orientation of axis. True

4.23

(a) For any arbitrary motion of a particle average velocity cannot be expressed by this equation. False

(b) The arbitrary motion of the particle can be represented by this equation, True

(c) For arbitrary motion of the particle, the acceleration may also be non uniform. False

(d) The motion of the particle is arbitrary, acceleration of the particle may also be non-uniform, so can not represent the motion of the particle in space. False

(e) The arbitrary motion of the particle can be represented by the given equation. True

Significance of de Broglie's Hypothesis in Modern Physics (NCERT-based answer):

De Broglie's hypothesis is a revolutionary idea which changed the understanding of matter and wave as we know it. This hypothesis introduced the concept that particles of matter, like electrons, and Proton, can behave like wave and have wave-like properties, just as light exhibits both wave and particle nature.

According to de Broglie, any moving particle has a wavelength given by:

$\lambda = \frac {h} {p} = \frac {h} {mv}$

where $\lambda$ is the wavelength, $h$ is Planck's constant, $m$ is the mass, and $v$ is the velocity of the particle.

2.3 

1 Calorie = 4.2 J = 4.2 kgm²s^-2

Standard formula for conversion

Given unit / New unit = (M1/M2)^x (L1/L2)^y (T1/T2)^z

Formula for energy = M¹L²T^-2

Here x = 1, y = 2, z = -2

In this problem

M1 = 1 kg, L1 = 1 m, T1 = 1 s and

M2 =? kg, L2 =? m, T2 =? s

So 1 Calorie = 4.2 (1/? )¹ (1/? )² (1/? )^-2

= 4.2? ^-1? ^-2? ²

8.12

Mass of the Sun, $M_s$ = $2*{10}^{30}$ kg, Mass of the Earth, $M_e$ = $6*{10}^{24}$ kg

Orbital radius, r = $1.5*{10}^{11}$ m

Let the mass of the rocket be, m

Let x be the distance from the centre of the Earth where the gravitational force acting on satellite P becomes zero.

From Newton's law of gravitation, we can equate gravitational forces acting on the satellite P under the influence of the Sun and the Earth as:

$\frac{G_m{M}_s}{({r-x)}^2}$ = $G_m\frac{M_e}{x^2}$ or( ${\frac{r-x}{x})}^2$ 

= $\frac{M_s}{M_e}$( ${\frac{r-x}{x})}^2$ = $\frac{{2*10}^{30}}{{6*10}^{24}}$ ,

 $\frac{r-x}{x}$ = 577.35 , r = 578.35x ,

x = $\frac{1.5*{10}^{11}}{578.35}$ = 2.59 $*{10}^8$ m

Ans.8.1

(a) No. Unlike electrical forces, gravitational force is independent of the status of the objects.

(b) Yes, the size of the space station is large enough and the astronaut will detect the change in Earth's gravity.

(c) Tidal effect depends inversely upon the cube of the distance while gravitational force depends inversely on the square of the distance. Since the distance between the Moon and the Earth is smaller than the distance between the Sun and the Earth, the tidal effect of the Moon's pull is greater than the tidal effect of the Sun's pull.