A projectile fired into the air suddenly explodes into several fragments. What can be said about the motion of the center of mass of the system made up of all the fragments after the explosion?

A projectile fired into the air suddenly explodes into several fragments. What can be said about the motion of the center of mass of the system made up of all the fragments after the explosion?

1. Center of mass of the system moves in the direction opposite to the direction of a fragment with the biggest mass,

2. Center of mass of the system moves in the direction of a fragment with the biggest mass,

3. Center of mass of the system moves in the direction of the biggest fragment,

4. Center of mass does not move,

5. Center of mass of the system follows the same parabolic path the projectile would have followed if there had been no explosion,

6. There is not enough information given.

7. Center of mass of the system moves in the direction opposite to the direction of a projectile just before it exploded.

The correct answer to the question is

5. Center of mass of the system follows the same parabolic path the projectile would have followed if there had been no explosion,'

Explanation:

To solve the question we note the following

1. Newton's first law of motion states that a body would continue in its path unless impressed upon by an unbalanced force

2. The source of the explosion is internal

3. Initial source of force = gravitational force hence motion parabola

4. The center of mass is the point in an object or specially distributed objects where the sum of the weighted mass is zero

5. An internal explosion will cause the particles to be distributed out based on their wight, that is the lighter weight  will travel farthest while the largest will remain closer to the center of mass

6. The above statement means that the center of mass does not change

7. Initial force of motion = mass × acceleration, with constant center of mass the path of the projectile is unchanged

Therefore

5. Center of mass of the system follows the same parabolic path the projectile would have followed if there had been no explosion,

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.