Here, $\gamma = 49 \times 10^{-5} K^{-1};$ $\Delta T = 30^{\circ}\mathrm{C}$ Let there be m grams of glycerine and its initial volume be $V$. Suppose that the volume of the glycerine becomes $V'$ after a rise of temperature of 30°C then,$V' = V (1 + \gamma \Delta T)$$= V (1 + 49 \times 10^{-5} \times 30)$ or $V' = 1.0147 V$Initial density of the glycerine, $\rho = \frac{m}{V}$Final density of the glycerine,$\rho' = \frac{m}{V'} = \frac{m}{1.0147 V}$$= \frac{\rho}{1.0147} = 0.9855 \rho$Therefore, fractional change in the value of density of glycerine,$\frac{\rho - \rho'}{\rho} = \frac{\rho - 0.9855 \rho}{\rho}$$= 0.0145$