Prof. Lewin in 23:17 in Lecture1 of Units,Dimensions and Scaling Arguments , in the equation of variation , Why did he multiply the factors of height , mass and gravitational acceleration ?? I am still a rookie in Physics , I am still 16 yrs old , so pls i need help quickly .
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he argues that time might be proportional to each of them separately, and thus would be proportional also to their product to some unknown power
He explains that ... the time taken for the object to fall is "PROPOTIONAL TO\[\alpha\]" So many factors, but for that instance, we take three factors
1. height at which the object is falling from so he takes H
2. M. mass of the object, which is falling (this is in relation to the famous question, is it the feather or the apple which reaches ground first from the same height).
3. Gravitational acceleration the more g is, fall will be faster (Value of g varies in various points of earth).
So he took the three factors,
Time \[\alpha\] Height,
T \[\alpha\] Mass,
T \[\alpha\] g ..
so, T \[\alpha\] H M and g.