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Question

(B) The given formula is $x = M^a L^b T^c$. Dimensional analysis states that if a quantity depends on $M, L,$ and $T$,it can be expressed in terms of

Vedclass · Accepted Answer

The dimension of $x$ cannot be expressed in terms of $M$ and $L$.

Vedclass · Answer

(B) The given formula is $x = M^a L^b T^c$. Dimensional analysis states that if a quantity depends on $M, L,$ and $T$,it can be expressed in terms of $M$ and $L$ only if the exponent of $T$ is zero (i.e.,$c = 0$). If $c 
eq 0$,the quantity $x$ essentially depends on the dimension of time $T$. Therefore,if $c 
eq 0$,the dimension of $x$ cannot be expressed solely in terms of $M$ and $L$ because the contribution of $T$ cannot be ignored or substituted by $M$ and $L$ unless there is a specific physical relationship between them.

$A$ physical quantity $x$ is represented by the formula $x = M^a L^b T^c$. If $c \neq 0$,then:

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