Question

v is directly proportional to g^x h^y where g is acceleration due to gravity, h=height. Find x and y.​

Answer 1

We gonna use dimensional method to solve.

Dimensions of velocity, v = LT^(-1)

Dimensions of acceleration, g = LT^(-2)

Dimensions of Length, h = L

given,

v = k g^x.h^y. k is proportionally constant

LT^(-1) = {LT^(-2)}^x . {L}^y

LT^(-1) = L^(x+y) . T^(-2x)

equating the exponents of respective dimensions

For T..

-2x = -1

x = 1/2

For L..

x+y = 1

y = 1/2

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