Question

Find the dimensions of a/b in the relation:
F= ax + bt ^2 , where F is force ,x is distance and t is time

Answer 1

Explanation:

ML/T^2=aL+bT^2

a=M/T^2

b=ML

a/b=L^-1T^-2

Answer 2

F = ax + bt^2

$f = ax \\ \\ a = \frac{f}{x} = \frac{ {m}^{1} {l}^{1} {t}^{ - 2} }{ {l}^{1} } \\ \\ a = {m}^{1} {t}^{ - 2} \\ \\ f = b {t}^{2} \\ \\ b = \frac{f}{ {t}^{2} } = \frac{ {m}^{1} {l}^{1} {t}^{ - 2} }{ {t}^{2} } = {m}^{ 1} {l}^{1} {t}^{ - 2} {t}^{ - 2} \\ \\ b = {m}^{ 1} {l}^{1} {t}^{ - 4}$

$\frac{a}{b} = \frac{ {m}^{1} {t}^{ - 2} }{ {m}^{1} {l}^{1} {t}^{ - 4} } \\ \\ \frac{a}{b} = {t}^{2} {l}^{ - 1}$

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