Why are space crafts usually launched from west to east? Why is it more advantageous to launch rockets in the equatorial plane?
Ans. Earth rotates on its axis from west to east. A satellite launched from west to east will have the advantage of the additional velocity of the earth’s rotation. The effect is maximum at the equator, hence it is most advantageous to launch the satellite from west to east on the equatorial plane.
INERTIAL AND GRAVITATIONAL MASSES:
(i) Inertial masses :– It is a measure of the ability of a body to oppose the production of acceleration in it by an external force. It also measure inertia of a body.
Let F be applied force on a body which produces an acceleration a
Then, F = ma
m = F/a
(i) Gravity has no effect on the inertial mass of the body
(ii) Inertial mass does not depends upon the size, shape and state of the body
(iii) Inertial mass of a body does not depend upon on the presence or absence of other bodies near it.
(iv) Inertial mass of a body is directly proportional to the quantity of matter contained in the body.
(v) Inertial mass of the body increases with increase in velocity.
Where mo is mass of a body at rest
v is velocity of the body
c is the velocity of the light in vacuum.
Gravitation of Mass :–
It is defined as mass of body which determines the magnitude of gravitational pull between the body and the earth. Let F be the gravitational force on a body of mass m due to earth
Then F = GMm/R2
Where R is the radius of earth
M is the mass of earth
m = FR2/GM
The mass of body determined in this way is the gravitational mass of the body.
Gravitational mass is same as inertial mass in all respect, except in the method of their measurement.
Reasons For Weightlessness :
Sol: 1. Any artificial satellite itself in a state of weightlessness condition becomes total earth gravitational force is balanced by centripetal force in order to orbiting the satellite in the given stable orbital.
2. Weightlessness conditions for any body placed inside the satellite can be employed in the following ways :
(a) Centrifugal force experienced by inside the body is neutralized by earth gravitational force.
(b) There is no normal reaction experienced by body from the surface to satellite because it is treated as point mass.
(c) Any body having zero relative acceleration with respect to satellite.
♦ Learn about : Moseley’s Law , Diffraction of X- Rays & Uses of X – Rays ♦
Moseley studied the characteristic X-ray spectrum of a number of a heavy elements, and observed a simple relationship between them. He found that the spectra of different elements are very similar, and with increasing atomic number Z , the spectral lines nearly shift towards shorter wavelength or higher frequencies.
He plotted a graph of the k-series between the square root of frequency (√ν)and atomic number (Z) and found it very approximately to be a straight line.
He therefore concluded that the square- root of the frequency of a K-line is closely proportional to the atomic number of the element. This is called Moseley’s Law and may be expressed as :
a = proportionality constant
b = screening constant
a and b does not depend on the nature of target.
Diffraction of X- Rays :-
(1) According to Laue the wavelength of X-Rays is very small and the atoms in crystals are arranged in form of three dimensional lattice.
(2) The diffraction of X-Rays is not possible by ordinary grating because the size of grating element is much larger than the wavelength of X-Rays.
(3) Diffraction of X-Rays is possible by the crystals. Because the inter atomic spacing in a crystal lattice is of the order of wavelength of X-Rays.
(4) Diffraction of X-Rays was first verified by laue spots.
(5) Diffraction of X-Rays takes place according to Bragg’s law
- (a) 2d sin θ = nλ
- (b) For maximum wavelength nmin = 1
(sin θ)max = 1
λmax = 2d
Uses of X – Rays
(i) In Study of crystal structure
(ii) In Surgery
(iii) In Medicine
(iv) In Spying
(v) In Engineering
(vi) In Research in the laboratories
(vii) In Industries
(viii) In Radiography
♦ Study about the Motion of Charged Particle Through Magnetic Field . The path of the particle in the magnetic field is circular ♦
The magnetic force equation gives, for a particle of charge q , mass m , velocity u, magnetic field B ,
The radius of the circular path is
Note : The figure shows a charged particle , moving in a Straight line , enters a region of magnetic field (field upwards). Once the particle is inside the field region, it experiences a magnetic force qvB . The path of the particle in the magnetic field is circular. Once it leaves the field region, the path becomes a straight line again. Let a screen is placed at a distance D from the centre of the field region. Then, the displacement OP’ , is X = D tanθ . It can be proved that tanθ = qBL/mu
Notice the difference, that when particle crosses a perpendicular electric field region, and hits the screen, the displacement observed is Y = qELD/mu2 while when it crosses a perpendicular magnetic field region and hits the screen, the displacement is X = qBLD/mu.