JEE Main 2015 · 11 Apr · Shift 1 · Physics Q9

← JEE Main 2015 · 11 Apr · Shift 1

PhysicsSingle correct+4 / -1Question 9 of 90

A beaker contains a fluid of density ρ kg/m $^3$ , specific heat S J/kg°C and viscosity η. The beaker is filled up to height h. To estimate the rate of heat transfer per unit area $(\dot Q/A)$ by convection when beaker is put on a hot plate, a student proposes that it should depend on η, $\left(\dfrac{S\Delta\theta}h\right)$ and $\left(\dfrac1{\rho g}\right)$ when Δθ (in °C) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for $(\dot Q/A)$ is :

\eta\dfrac{S\Delta\theta}h

\eta\left(\dfrac{S\Delta\theta}h\right)\left(\dfrac1{\rho g}\right)

\dfrac{S\Delta\theta}{\eta h}

\left(\dfrac{S\Delta\theta}{\eta h}\right)\left(\dfrac1{\rho g}\right)

Answer and worked solution

Official answer: A

Check dimensions. $\eta$ is kg m⁻¹ s⁻¹ and $\dfrac{S\Delta\theta}h$ is (J/kg)/m $=$ m s⁻². Their product is kg s⁻³ $=$ W m⁻², the unit of $\dot Q/A$ . Adding $\frac1{\rho g}$ would spoil the dimensions, so
$\frac{\dot Q}A=\eta\frac{S\Delta\theta}h.$

Topics:Dimensional analysis Convection

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JEE Main 2015 · 11 Apr · Shift 1, Physics question 9