If energy( $E$ ), velocity ( $V$ ) and force ( $F$ ) be taken as fundamental quantity, then what are the dimension of mass ?

E V^{2}

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E V^{- 2}

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F V^{- 1}

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F V^{- 2}

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Solution

The correct option is B $E V^{- 2}$
We know that,
$[E] = M L^{2} T^{- 2}$
$[v] = M^{0} L^{1} T^{- 1}$
$[F] = M^{1} L^{1} T^{- 2}$
$L e t d i m e n s i o n o f m a s s i n E i s = x$
$L e t d i m e n s i o n o f m a s s i n V i s = y$
$L e t d i m e n s i o n o f m a s s i n F i s = z$
Then, $M = E^{x} V^{y} F^{z}$
$M^{1} L^{0} T^{0} = [M L^{2} T^{- 2}]^{x} [M^{0} L^{1} T^{- 1}]^{y} [M^{1} L^{1} T^{- 2}]^{z}$
$M^{1} L^{0} T^{0} = M^{x + z} L^{2 x + y + z} T^{- 2 x - y - 2 z}$
$x + z = 1 . . . . . . . . . . . . . . . (i)$
$2 x + y + z = 0 . . . . . . . . . . . . . . . (i i)$
$2 x + y + 2 z = 0 . . . . . . . . . . . . . . . (i i i)$
By equation (i), (ii) & (iii)
$x = 1$
$y = - 2$
$z = 0$
So, $[M] = E^{1} V^{- 2} .$

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If energy (E), velocity (v) and force (F) be taken as fundamental quantity, then what are the dimensions of mass

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