Question

The units of three physical quantities $x,y$ and $z$ are $gc{m}^2{s}^{-5},g{s}^{-1}$ and $cm{s}^{-2}$ respectively. The relation between $x,y$ and $z$ is

• A. $z=x^{2}y$
• B. $y^2=xz$
• C. $x=y{z}^2$
• D. $x=y^{2}z$

Answer 1

The correct option is C $x=y{z}^2$

Let the relation be $x^a=y^b{z}^c$.

Now putting the units in this expression,

$({g{cm}^2{s}^{-5})}^a={\left(g{s}^{-1}\right)}^b{\left(cm{s}^{-2}\right)}^c$

Equating the powers of various quantities independently, we get

$a=b$

$2a=c$

$5a=b+2c$

Solving these equations and putting in the original expression, we get $x=y{z}^2$.