Question

If velocity (V), force (F) and energy (E) are taken as fundamental units, then dimensional formula for mass will be

• A. $V^{- 2}F^{0}E$
• B. $V^{0}FE^{2}$
• C. $VF^{- 2}E^{0}$
• D. $V^{- 2}F^{0}E$

Answer 1

Answer: (D)

$V^{- 2}F^{0}E$

Answer 2

Let $M = V^{a}F^{b}E^{c}$

Putting dimensions of each quantities in both side $\lbrack M\rbrack = \lbrack LT^{- 1}\rbrack^{a}\lbrack MLT^{- 2}\rbrack^{b}\lbrack ML^{2}T^{- 2}\rbrack^{c}$

Equating powers of dimensions. We have $b + c = 1,$ $a + b + 2c = 0$ and $- a - 2b - 2c = 0$

Solving these equations, $a = - 2,$ b = 0 and c = 1

So $M = \lbrack V^{- 2}F^{0}E\rbrack$