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Question

Two bodies having volumes $$V$$ and $$2V$$ are suspended from the two arms of a common balance and they are found to balance each other. If larger body is immersed in oil (density $${ d }_{ 1 }=0.9gm/{ cm }^{ 3 }$$) and the smaller body is immersed in an unknown liquid, then the balance remain in equilibrium. The density of unknown liquid is given by


A
2.4gm/cm3
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B
1.8gm/cm3
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C
0.45gm/cm3
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D
2.7gm/cm3
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Solution

The correct option is B $$1.8gm/{ cm }^{ 3 }$$
Two bodies are found to balance each other even after these are dipped in liquids of different densities, which means they have displaced the equal weights of liquids.
Weight of the oil displaced by larger block $$=2V \times 0.9 \times g$$  .........$$(I)$$
Weight of the unknown liquid displaced by smaller block $$=V \times \rho \times g$$  .........$$(II)$$
Equating $$(I)$$ and $$(II)$$, we have
$$\rho=1.8\ gm/cm^3$$

Physics

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