In an experiment, students roll several hoops down the same incline plane. Each hoop has the same mass but a different radius. Each hoop rolls down the incline without slipping. Which of the following graphs best shows the linear speed V of the hoops at the bottom of the incline as a function of the radius r of the hoop?

The graph should have velocity (v) on the y-axis and radius (r) on the x-axis. It will have a straight, horizontal line that goes across the graph.

Explanation:

Shown above is the formula for Kinetic Energy in rotational terms. I'm new to brain.ly so I couldn't insert the omega symbol, sorry about that. Omega can be replaced with . Moment of Inertia (I) can be replaced with .

The equation becomes .

The r's cancel out, making the different radii negligible, causing a straight horizontal line.

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.