Question

The dimension of $K$ in the equation $W=\frac{1}{2}K{x}^2$ is

• A. $\left[M^1{L}^0{T}^{-2}\right]$
• B. $\left[M^0{L}^1{T}^{-1}\right]$
• C. $\left[M^1{L}^1{T}^{-2}\right]$
• D. $\left[M^1{L}^0{T}^{-1}\right]$

Answer 1

Answer: (A)

$W=\frac{1}{2}k{x}^2$
Writing the dimensions on both sides
$[M{L}^2{T}^{-2}]=k[M^0{L}^2{T}^0]$
$\therefore$ Dimension of $k=[M{L}^{-2}]=[M{L}^0{T}^{-2}]$