Question

Position of a body with acceleration $a$ is given by $x=k{a}^m{t}^n$, here $t$ is time, find the 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

Answer 1

Answer: (B)

Position $x=K{a}^m{t}^n$
Writing the dimension on the both sides.
$\left[M^{0}L{T}^0\right]={\left[L{T}^{-2}\right]}^m[T{]}^n$
$\left[M^0{L}^m{T}^{-2m+n}\right]$
On comparing both sides.
$m=1$
$-2m+n=0$
$n=2m=2\times 1=2$