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A man wlaking briskly in rain with speed v must slant his umbrella forward making an angle theta with the vertical . A student derives the following relation between theta and v : <br> tan theta=v <br> and checks that the relations has a correct limit : as v rarr 0, theta rarr 0 , as expected . (We are assuming there is no string wing and that the rains falls vertically for a stationary man). Do you think this relation can be correct ? If not, guess at the correct relation .

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Answer Text

Solution :
According to principle of homogenity of dimensional equations, Dimensions of `L.H.S. =` Dimensions of `R.H.S.` <br> Here, `v =tan theta` <br> i.e., `[L^(1) T^(-1)] =` dimensionless, which is incorrect <br> Correcting the `L.H.S.` we. Get <br> `v//u=tan theta`, where u is velocity of rain.

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