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 $n$.
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 $n$.
$m = 1$, $n = 1$
$m = 1,\;n = 2$
$m = 2,\;n = 1$
$m = 2,\;n = 2$
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 $n$.
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$ $⇒$ $n = 2$.