Question

A physical quantity $x$ can be dimensionally represented in terms of $M,L$ and $T$ is $x=M^a{L}^b{T}^c$. The quantity time

• A. may be dimensionally represented in terms of $x,M$ and $L$ if $c$ $\ne$ 0.
• B. may be dimensionally represented in terms of $x,M$ and $L$ if $c=0$.
• C. may be dimensionally represented in terms of $x,M$ and $L$, irrespective of $c$.
• D. may be dimensionally represented in terms of $x,M$ and $L$.

Answer 1

The correct option is A may be dimensionally represented in terms of $x,M$ and $L$ if $c$ $\ne$ 0.

A derived quantity can always be represented in terms of base quantities and vice-versa. Thus for X to be a derived quantity of time, C can't be zero. In that case time may be represented in terms of derived quantity and remaining base quantities. If c=0, then it's not possible because derived quantity X will be independent of time and vice-versa.