Position of a body with acceleration ' a ' is given by x = K{a^m}{t^n}, here t is time. Find

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1.Units, Dimensions and Measurement

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Position of a body with acceleration '$a$' is given by $x = K{a^m}{t^n},$ here $t$ is time. Find dimension of $m$ and $n$.

A

$m = 1$, $n = 1$

B

$m = 1,\;n = 2$

C

$m = 2,\;n = 1$

D

$m = 2,\;n = 2$

Solution

(b) As $x = K{a^m} \times {t^n}$

$\left[ {{M^0}L{T^0}} \right] = {\left[ {L{T^{ – 2}}} \right]^m}{\left[ T \right]^n} = \left[ {{L^m}{T^{ – 2m + n}}} \right]$

$\therefore $ $m = 1$ and $ – 2m + n = 0$ $⇒$ $n = 2$.

Standard 11

Physics

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