If force F , power P and impulse J are taken as the fundamental quantities in a system, then dimensional formula of length in this system is given by $[F^{x} P^{y} J^{z}]$ . Find $x + y + z$

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Detailed Solution

$M^{0} L^{1} T^{0} = {[M^{1} L^{1} T^{- 2}]}^{a} {[M^{1} L^{2} T^{- 3}]}^{b} {[M^{1} L^{1} T^{- 1}]}^{c} \begin{array}{l} a = - 2, b = c = 1 \\ x + y + z = 0 \end{array}$

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