4. suppose the pendulum of a grandfather clock expands because of heat. will it overcount or undercount time?

under count

Explanation:

Time period of simple pendulum clock is given by

where L=length of pendulum

g=acceleration due to gravity

With increase in temperature there is increase in length as material expands with increasing temperature

and time period is inversely proportional to the square root of length therefore time period decreases and it under counts time  

kepler used the data from tycho blahe (his mentor) to construct the laws of planetary motion.

as we know our atmosphere or air have different levels. every level has other gasses, and every gas has another permeability. when the light comes from lower permeability to higher permeability, it changes its direction. so that means that when the light comes from the moon to the earth, it changes it's direction many more times. it basically means that the shape of the light part of the moon is changed on the earth.

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