If force (F), velocity (V) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be [2023]

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Solution

Q.
If force (F), velocity (V) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be [2023]

1 $F V^{- 2} T^{2}$

2 $F V^{- 4} T^{2}$

3 $F V^{4} T^{- 6}$

4 $F^{2} V^{- 2} T^{6}$

Ans.
(2)

$[M L^{- 3}] = {[M L T^{- 2}]}^{a} {[L T^{- 1}]}^{b}$ ${[T]}^{c} = [M^{a} L^{a + b} T^{- 2 a + b + c}]$

a = 1

a + b = –3 $\Rightarrow$ b = –4

Also, – 2a – b + c = 0

c = 2

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