Question

Position of a body with acceleration a is given by $x=k{a}^m{t}^n$ . Here, $t$ is time. Find the values 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

The correct option is B

$m=1,n=2$

Step 1: Given Data:

Position of a body with acceleration a is given by-

$x=k{a}^m{t}^n$

Step 2: Formula used:

The dimensional formula of distance $x=\left[M^{0}L{T}^0\right]$

Dimensional formula of acceleration $a=\left[M^{0}L{T}^{-2}\right]$

Dimensional formula of time $t=\left[M^0{L}^{0}T\right]$

Step 3: Calculating the values of m and n:

$x=k{a}^m{t}^n$

Now on further solving and substituting the values,

$\begin{array}{rcl}\left[M^{0}L{T}^0\right]& =& {\left[L{T}^{-2}\right]}^m{\left[T\right]}^n\\ \left[M^{0}L{T}^0\right]& =& \left[L^m{T}^{-2m+n}\right]\end{array}$

Step 3: Comparing the L.H.S and R.H.S term

On comparing the left-hand side term and right-hand side term we get-

$$\begin{gathered} m=1 \\ -2m+n=0 \\ n=2 \end{gathered}$$

Thus, the values are $m=1,n=2$

Hence option (B) is the correct answer.