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The energy E of a system is function of time t and is given by $E (t) = αt - {βt}^{3}$ where $α$ and $β$ are constants. The dimensions of $α$ and $β$ are

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[ML²T^-3] and [ML²T^-5]

[ML²T^-1] and [ML²T]

[LT^-1] and [LT]

[MLT^-1] and [MLT]

answer is C.

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Detailed Solution

$\begin{array}{l} [α] [t] = [E] \\ [α] [t] = [M^{2} T^{- 2}] \\ [α] = [M^{2} T^{- 3}] \\ [B] [t^{3}] = [E] \\ B = [{ML}^{2} T^{- 5}] \end{array}$

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