Physics And Measurement Question 161

Question: In a system of units if force (F), acceleration and time (T) are taken as fundamental units then the dimensional formula of energy is?

[BHU 2005]

Options:

A) $ FA^{2}T $

B) $ FAT^{2} $

C) $ F^{2}AT $

D) $ FAT $

Show Answer

Answer:

Correct Answer: B

Solution:

$ E=KF^{a}A^{b}T^{c} $

$ [ ML^{2}{{T}^{-2}} ]={{[ ML{{T}^{-2}} ]}^{a}}{{[ L{{T}^{-2}} ]}^{b}}{{[ T ]}^{c}} $

$ [ ML^{2}{{T}^{-2}} ]=[ M^{a}{{L}^{a+b}}{{T}^{-2a-2b+c}} ] $

$ \therefore $ $ a=1 $ , $ a+b=2 $

therefore $ b=1 $ and $ -2a-2b+c=-2\ \ \Rightarrow \ c=2 $

$ \therefore $ $ E=KFAT^{2} $ .



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