Question

a circular cap ( radius 1 cm ) of a bottle floats in benzene ( density 0.92 g / cm^3) upside down. when apiece of chalk is place on it, it sinks by 1 mm. find the mass of chalk. define density.

Answer 1

$$\begin{gathered} \mathrm{Density}:\mathrm{It}\mathrm{is}\mathrm{the}\mathrm{ratio}\mathrm{of}\mathrm{mass}\mathrm{of}\mathrm{a}\mathrm{body}\mathrm{to}\mathrm{its}\mathrm{volume}. \\ \mathrm{From}\mathrm{Archimedes}\mathrm{principle}, \\ \mathrm{Weight}\mathrm{of}\mathrm{the}\mathrm{chalkpiece}=\mathrm{Weight}\mathrm{of}\mathrm{the}\mathrm{liquid}\mathrm{displaced}\mathrm{due}\mathrm{to}\mathrm{volume}\mathrm{immersed} \\ {\mathrm{m}}_{\mathrm{chalk}}\mathrm{g}={\mathrm{m}}_{\mathrm{liquid}}\mathrm{g} \\ {\mathrm{m}}_{\mathrm{chalk}}={\mathrm{m}}_{\mathrm{liquid}} \\ ={\mathrm{d}}_{\mathrm{liquid}}△{\mathrm{V}}_{\mathrm{liquid}} \\ ={\mathrm{d}}_{\mathrm{liquid}}\times {\mathrm{\pi r}}^2\mathrm{h} \\ =0.92\times \mathrm{\pi }\times 1^2\times 0.1[\mathrm{since}1\mathrm{mm}=0.1\mathrm{cm}] \\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{29}\mathbf{}\mathbf{g} \end{gathered}$$