Q: A quantity X is defined by the equation X = 3 CB^{2}, where C is capacitance in farad and B is magnetic field in tesla. The dimension of mass in X is:

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Ans: 1

Sol: $\displaystyle X = 3 C B^2 $ ….(i)

$\displaystyle C = \frac{q}{V} $

$\displaystyle B = \frac{F}{q v} $ ; (Since , F = q v B )

From (i)

$\displaystyle X = \frac{q}{V} \times (\frac{F}{q v})^2 $

$\displaystyle X = \frac{q}{W/q} \times (\frac{F}{q v})^2 $ ; (Since , W = V q)

$\displaystyle X = \frac{q}{W/q} \times (\frac{F}{q v})^2 $

$\displaystyle X = \frac{F^2}{W v^2} $

$\displaystyle X = \frac{[M L T^{-2}]^2}{[M L^2 T^{-2}] [LT{-1}]^2} $

$\displaystyle X = \frac{[M^2 L^2 T^{-4}]}{[M L^4 T^{-4}]|} $

$\displaystyle X = [M^1 L^{-2}] $