Two systems are in oscillation: a simple pendulum swinging back and forth through a very small angle and a block oscillating on a spring. The block-spring system takes twice as much time as the pendulum to complete one oscillation. What could be done to make the two systems oscillate with the same period

Here to make the two systems oscillate with same period either decrease the mass of the block system to one fourth or increase the length of the string to four times

Explanation:

we know that time period of block spring system is  

   where m = mass of the block

              k= spring constant

      and also time period of simple pendulum making small oscillations  is

      where l = length of the pendulum    

                 g = acceleration due to gravity

   so here to make time period of the both systems to be same either we can decrease the block system time period to its half or double the time period of the pendulum.

 To decrease the time period of block spring system to half its value from above equation we need to decrease the mass of the block to one fourth

 and to increase the time period of the pendulum we need to increase length by four times .

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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.