Question

The dimension of k in the equation w =1/2 kx square

Answer 1

w=1/2kx square
w/x square =k
ML2T-2 /(L)square=k
ML2T-2 L-2=k
ML0T-2=k
here L is L raised power 0
T-2 is T raised power -2
hence dimensional formula of k is [ML0T-2]

Answer 2

Answer:

The dimensional formula of k is $[MT^{-2}]$

Explanation:

Here, we need to write the dimension formula of k in the given formula as :

$W=\dfrac{1}{2}kx^2$

Where

k is the spring constant

x is the compression or stretching in spring

$k=\dfrac{2W}{x^2}$

The dimension formula of W is, $[W]=[ML^2T^{-2}]$

The dimension formula of x² is, $[x^2]=[L^2]$

So, the dimensional formula of k is :

$k=\dfrac{[ML^2T^{-2}]}{L^2}$

$[k]=[MT^{-2}]$

Hence, this is the required solution.