At 0^ ^ ^ C , the densities of wood and benzene are 880 kg m^ -3...

For the piece of wood to just sink in benzene, the density of the wood must become equal to the density of benzene at that temperature $T$.

The density of a substance at temperature $T$ is given by:
$\rho_T = \dfrac{\rho_0}{1 + \gamma T}$

Equating the densities of wood and benzene at temperature $T$:
$\rho_{wT} = \rho_{bT}$

$\dfrac{\rho_{w0}}{1 + \gamma_w T} = \dfrac{\rho_{b0}}{1 + \gamma_b T}$

Cross-multiplying, we get:
$\rho_{w0} (1 + \gamma_b T) = \rho_{b0} (1 + \gamma_w T)$

Substituting the given values:
$880 (1 + 1.5 \times 10^{-3} T) = 900 (1 + 1.2 \times 10^{-3} T)$

$880 + 880 \times 1.5 \times 10^{-3} T = 900 + 900 \times 1.2 \times 10^{-3} T$

$880 + 1.32 T = 900 + 1.08 T$

$1.32 T - 1.08 T = 900 - 880$

$0.24 T = 20$

T = \dfrac{20}{0.24} = \dfrac{2000}{24} = 83.33^{}^{{}^{\circ}}\text{C}

Rounding to the nearest integer, the temperature is 83^{}^{{}^{\circ}}\text{C}.