Question

A physical quantity $x$ can be dimensionally represented in terms of $M,L$ and $T$ that 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 value of $c$
• D. can never be dimensionally represented in terms of $x,M$ and $L$

Answer 1

Answer: (A)

may be dimensionally represented in terms of $x,M$ and $L$ if $c\ne 0$

To represent time in powers of $x,M,L$ following relation must satisfy,

$x^n{M}^A{L}^B=T$

$M^{na+A}{L}^{nb+B}{T}^{nc}=T$

Clearly this is true if $A=-na,B=-nb$ and $c=\frac{1}{n}$. Hence c has to be non zero for time to be represented in terms of $x,M,L$.