A physical quantity $$\zeta $$ is calculated using the formula $$\zeta = \frac{{\frac{1}{{10}}x{y^2}}}{{{z^{\frac{1}{3}}}}},$$ where $$x,y$$ and $$z$$ are experimentally measured quantities. If the fractional error in the measurement of $$x,y$$ and $$z$$ are $$2\% ,1\% $$ and $$3\% $$ respectively, then the fractional error in $$\zeta $$ will be
A quantity $$X$$ is given by $${\varepsilon _0}L\frac{{\Delta V}}{{\Delta t}}$$ where $${ \in _0}$$ is the permittivity of the free space, $$L$$ is a length, $$\Delta V$$ is a potential difference and $$\Delta t$$ is a time interval. The dimensional formula for $$X$$ is the same as that of-
Pressure depends on distance as, $$P = \frac{\alpha }{\beta }exp\left( { - \frac{{\alpha z}}{{k\theta }}} \right),$$ where $$\alpha ,$$ $$\beta $$ are constants, $$z$$ is distance, $$k$$ is Boltzman’s constant and $$\theta $$ is temperature. The dimension of $$\beta $$ are-