Units & Dimensions

JEE Main level, single correct, medium

50 of 149

Question 50 of 149

Which one of the following is the correct dimensional formula for the capacitance in F ? M,L,T\mathrm{M}, \mathrm{L}, \mathrm{T} and C stand for unit of mass, length, time and charge,

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Answer: (A) [F]=[C2M−1 L−2 T2][\mathrm{F}]=\left[\mathrm{C}^2 \mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^2\right]

 Energy =Q22C∴[F]=[C2][ML2 T−2]=[C2M−1 L−2 T+2]\begin{aligned} & \text { Energy }=\frac{Q^2}{2 C} \\ & \begin{aligned} \therefore \quad[\mathrm{F}] & =\frac{\left[\mathrm{C}^2\right]}{\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]} \\ & =\left[\mathrm{C}^2 \mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{+2}\right]\end{aligned}\end{aligned}

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