The following observations were taken for determining surface tension $$T$$ of water by capillary method:
Diameter of capillary, $$D = 1.25 \times {10^{ - 2}}m$$
Rise of water, $$h = 1.45 \times {10^{ - 2}}m$$
Using $$g = 9.80\,m/{s^2}$$ and the simplified relation $$T = \frac{{rgh}}{2} \times {10^3}N/m,$$ the possible error in surface tension is closest to-
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-