A) \[\left[ p{{v}^{2}}{{t}^{2}} \right]\]
B) \[\left[ {{p}^{-1}}{{v}^{2}}{{t}^{-2}} \right]\]
C) \[\left[ pv{{t}^{2}} \right]\]
D) \[\left[ {{p}^{-1}}v{{t}^{2}} \right]\]
Correct Answer: C
Solution :
Let\[F\propto {{P}^{x}}{{v}^{y}}{{T}^{z}}\] \[[p]=[M{{L}^{-1}}{{T}^{-2}}],[v]=[L{{T}^{-1}}],[t]=[T]\] Comparing the dimension of both sides \[x=1,\text{ }y=2,z=2\] So, \[F=p{{v}^{2}}{{t}^{2}}\]
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