A) \[[L{{T}^{-4}}]\,and\,[L{{T}^{-1}}]\]
B) \[[L{{T}^{-1}}]\,and\,[L{{T}^{-4}}]\]
C) \[[ML{{T}^{-4}}]\,and\,[ML{{T}^{-1}}]\]
D) \[[MLT]\,and\,[ML{{T}^{-4}}]\]
E) \[[ML{{T}^{-3}}]\,and\,[ML{{T}^{-2}}]\]
Correct Answer: D
Solution :
By the principal of dimensions homogenety \[F=a{{t}^{-1}}\] \[[ML{{T}^{-2}}]=a[{{T}^{-1}}]\] \[\therefore \] \[a=[ML{{T}^{-1}}]\] Similarly for \[b=[ML{{T}^{-4}}]\] So, \[[ML{{T}^{-1}}],[ML{{T}^{-4}}]\]
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