First slide

Dimensions of physical quantities

Question

If frequency F, velocity V, and density D are considered fundamental units, the dimensional formula for momentum will be

Moderate

A

$D V F^{2}$
B

$D V^{2} F^{- 1}$
C

$D^{2} V^{2} F^{2}$
D

$D V^{4} F^{- 3}$

Solution

$\begin{array}{l} Momentum, p = m v = M L T^{- 1} = M L^{- 3} L^{4} T^{- 4} T^{3} \\ = D V^{4} F^{- 3} \\ ∵ d i m e n s i o n a l f o r m u l a f o r d e n s i t y i s M L^{- 3}; d i m e n s i o n a l f o r m u l a f o r v e l o c i t y i s L T^{- 1} a n d f o r f r e q u e n c y F i s T^{- 1} \end{array}$

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