A) \[P{{V}^{2}}{{T}^{2}}\]
B) \[{{P}^{-1}}{{V}^{2}}{{T}^{-2}}\]
C) \[PV{{T}^{2}}\]
D) \[{{P}^{-1}}V{{T}^{2}}\]
Correct Answer: A
Solution :
Let \[F\propto {{P}^{x}}{{V}^{y}}{{T}^{z}}\] by substituting the following dimensions : \[[P]=[M{{L}^{-1}}{{T}^{-2}}]\]\[[V]=[L{{T}^{-1}}],\,[T]=[T]\] and comparing the dimension of both sides \[x=1,\,y=2,\,z=2\], so \[F=P{{V}^{2}}{{T}^{2}}\]
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