In the formula X = 3YZ2, X and Z have dimensions of capacitance and magnetic induction respectively. The dimensions of Y in MKSQ system are

Question

In the formula X = 3YZ2, X and Z have dimensions of capacitance and magnetic induction respectively. The dimensions of Y in MKSQ system are (A) [M-3L-2T4Q4] (B) [M-2L-1T5Q3] (C) [M-1L-2T4Q4] (D) [M-3L-1T4Q4]

Tardigrade Admin · Accepted Answer

x =3 yz 2 x = M -1 L -2 I 2 T 4 z = M 1 I -1 T -2 Let, y = M α L β T &gamma; Q δ ( M -1 L -2 I 2 T 4)=( M α L β T &gamma; Q δ)( M +1 L 0 I -1 T -2) IT = Q α=-3, β=-2, &gamma;=4, δ=4 y = M -3 L -2 T 4 Q 4

Q. In the formula $X = 3 Y Z^{2}$ , $X$ and $Z$ have dimensions of capacitance and magnetic induction respectively. The dimensions of $Y$ in $M K SQ$ system are

$[M^{- 3} L^{- 2} T^{4} Q^{4}]$

$[M^{- 2} L^{- 1} T^{5} Q^{3}]$

$[M^{- 1} L^{- 2} T^{4} Q^{4}]$

$[M^{- 3} L^{- 1} T^{4} Q^{4}]$

$x = 3 y z^{2}$
$x = M^{- 1} L^{- 2} I^{2} T^{4}$
$z = M^{1} I^{- 1} T^{- 2}$
Let, $y = M^{α} L^{β} T^{γ} Q^{δ}$
$(M^{- 1} L^{- 2} I^{2} T^{4}) = (M^{α} L^{β} T^{γ} Q^{δ}) (M^{+ 1} L^{0} I^{- 1} T^{- 2})$
$I T = Q$
$α = - 3, β = - 2, γ = 4, δ = 4$
$y = M^{- 3} L^{- 2} T^{4} Q^{4}$

Q. In the formula X=3YZ2, X and Z have dimensions of capacitance and magnetic induction respectively. The dimensions of Y in MKSQ system are

[M−3L−2T4Q4]

[M−2L−1T5Q3]

[M−1L−2T4Q4]

[M−3L−1T4Q4]