Question bank/JEE Main/Physics

The densities of wood and benzene at 0°C
are$\ 880{kgm}^{- 3}$and $\ 900\ {kgm}^{- 3}$, respectively. The
coefficients of volume expansion of wood is
$1.2 \times 10^{- 3^{{^\circ}}}C^{- 1}$ and that of benzene is
$1.5 \times 10^{- 3^{{^\circ}}}C^{- 1}$. Value of temperature (in °C) at
which a piece of this wood would just sink in benzene at the same
temperature is T. Then find value of [IMAGE] (where T is
temperature in °C).

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For just sink condition
$\rho_{ow\ }\left( 1 - \gamma_{w\ }\Delta T \right) = \rho_{ob\ }\left( 1 - \gamma_{b}\Delta T \right)$
$880\left( 1 - 1.2 \times 10^{3}(T - 0) \right) = 900\left( 1 - 1.5 \times 10^{- 3}(T - 0) \right)$
$T10^{- 3}(1.5 - 1.2) = 900 - 880$
$T \times 10^{- 3} \times 0.3 = 20$
$T = \frac{20 \times 10^{4}}{3}{^\circ}C$

Source: Grass-G / P-24 Physcis Paper 31 Dec.docx