quick-short-Q-2-things-are-mixed-1-both-same-volume-2-both-same-mass-density-d-v-and-d-m-d-v-d-m-lt-or-gt-

Question Number 225625 by fantastic last updated on 04/Nov/25

$${quick}\:{short}\:{Q} \\ $$$$\mathrm{2}\:{things}\:{are}\:{mixed}\: \\ $$$$\left.\mathrm{1}\right){both}\:{same}\:{volume} \\ $$$$\left.\mathrm{2}\right){both}\:{same}\:{mass} \\ $$$${density}\Rightarrow{d}_{{v}} \:{and}\:{d}_{{m}} \\ $$$${d}_{{v}} \:?\:{d}_{{m}} \left[=,<\:{or}>\right] \\ $$

Commented by mahdipoor last updated on 04/Nov/25

$$\mathrm{V}_{\mathrm{1}} =\mathrm{V}_{\mathrm{2}} \:\:\:\mathrm{and}\:\:\mathrm{m}_{\mathrm{1}} =\mathrm{m}_{\mathrm{2}} \:\:\:\Rightarrow\rho_{\mathrm{1}} =\frac{\mathrm{m}_{\mathrm{1}} }{\mathrm{V}_{\mathrm{1}} }=\frac{\mathrm{m}_{\mathrm{2}} }{\mathrm{V}_{\mathrm{2}} }=\rho_{\mathrm{2}} \\ $$

Commented by fantastic last updated on 04/Nov/25

$${no}\:{no}\:{sir} \\ $$$${they}\:{are}\:{different}\:{cases} \\ $$

Commented by mahdipoor last updated on 04/Nov/25

$$\mathrm{case}\:\mathrm{1}\: \\ $$$$\mathrm{d}_{\mathrm{V}} =\frac{\mathrm{d}_{\mathrm{1}} \mathrm{V}+\mathrm{d}_{\mathrm{2}} \mathrm{V}}{\mathrm{2V}}=\frac{\mathrm{d}_{\mathrm{1}} +\mathrm{d}_{\mathrm{2}} }{\mathrm{2}} \\ $$$$\mathrm{case}\:\mathrm{2} \\ $$$$\mathrm{d}_{\mathrm{m}} =\frac{\mathrm{m}+\mathrm{m}}{\frac{\mathrm{m}}{\mathrm{d}_{\mathrm{1}} }+\frac{\mathrm{m}}{\mathrm{d}_{\mathrm{2}} }}=\frac{\mathrm{2d}_{\mathrm{1}} \mathrm{d}_{\mathrm{2}} }{\mathrm{d}_{\mathrm{1}} +\mathrm{d}_{\mathrm{2}} } \\ $$$$\mathrm{d}_{\mathrm{m}} \:?\:\mathrm{d}_{\mathrm{V}} \:\Rightarrow\:\frac{\mathrm{2d}_{\mathrm{1}} \mathrm{d}_{\mathrm{2}} }{\mathrm{d}_{\mathrm{1}} +\mathrm{d}_{\mathrm{2}} }\:?\:\frac{\mathrm{d}_{\mathrm{1}} +\mathrm{d}_{\mathrm{2}} }{\mathrm{2}}\:\Rightarrow\:\mathrm{4d}_{\mathrm{1}} \mathrm{d}_{\mathrm{2}} \:?\:\left(\mathrm{d}_{\mathrm{1}} +\mathrm{d}_{\mathrm{2}} \right)^{\mathrm{2}} \\ $$$$\Rightarrow\:\mathrm{0}\:?\:\left(\mathrm{d}_{\mathrm{1}} −\mathrm{d}_{\mathrm{2}} \right)^{\mathrm{2}} \:\:\Rightarrow\:?\equiv\leqslant\:\Rightarrow\:\mathrm{d}_{\mathrm{m}} \leqslant\mathrm{d}_{\mathrm{V}} \\ $$$$\begin{cases}{\mathrm{if}\:\:\:\mathrm{d}_{\mathrm{1}} =\mathrm{d}_{\mathrm{2}} \:\:\Rightarrow\:\mathrm{d}_{\mathrm{m}} =\mathrm{d}_{\mathrm{V}} }\\{\mathrm{else}\:\:\mathrm{d}_{\mathrm{m}} <\mathrm{d}_{\mathrm{V}} }\end{cases} \\ $$

Commented by fantastic last updated on 05/Nov/25

$${correct}\:{sir} \\ $$

Terms of Service
Privacy Policy
Contact: info@tinkutara.com