JEE Main 2015 — Units and Dimensions Question with Solution

A beaker contains a fluid of density $\rho$$\frac{kg}{m^3}$ , specific heat $S\frac{J}{k{g}^{o}C}$ and viscosity $\eta$ . The beaker is filled up to height h. To estimate the rate of heat transfer per unit area $\left(\frac{\dot{Q}}{A}\right)$ by convection when beaker is put on a hot plate, a student proposes that it should depend on $\eta$ , $\left(\frac{S\mathrm{\Delta }\theta }{h}\right)$ and $\left(\frac{1}{\rho g}\right)$ when $\mathrm{\Delta }\theta$ ( ${\mathrm{i}\mathrm{n}}^{o}C$ ) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for $\left(\frac{\dot{Q}}{A}\right)$ is: