Alarge, 42.0 kg bell is hung from a wooden beam so it can swing back and forth with negligible friction. the bell's center of mass is 0.80 m below the pivot. the bell's moment of inertia about an axis at the pivot is 18.0 kg⋅m2. the clapper is a small, 1.8 kg mass attached to one end of a slender rod that has length l and negligible mass. the other end of the rod is attached to the inside of the bell; the rod can swing freely about the same axis as the bell. what should be the length l of the clapper rod for the bell to ring silently that is, for the period of oscillation for the bell to equal that of the clapper?

0.11 m/s and 0.28 m/s should be correct

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.