SATHEE: Properties of Matter 2 Question 2

Properties of Matter 2 Question 2

2. A wooden block floating in a bucket of water has $\frac{4}{5}$ of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is (2019 Main, 9 April II)

(a) 0.6

(b) 0.8

(d) 0.5

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Answer:

Correct Answer: 2. (a)

Solution:

(a) For a floating body,

upthrust $=$ weight of the part of object, i.e. submerged in the fluid.

In first situation,

So, weight of block of volume $V =$ weight of water of volume $\frac{4}{5} V \Rightarrow V ρ_{b} g = \frac{4}{5} V ρ_{w} g$

where, $ρ_{b} =$ density of block

and $ρ_{w} =$ density of water.

$\Rightarrow \frac{ρ_{b}}{ρ_{w}} = \frac{4}{5}$

In second situation,

So, weight of block of volume $V =$ weight of oil of volume $\frac{V}{2} +$ weight of water of volume $\frac{V}{2}$ .

$\Rightarrow V ρ_{b} g = \frac{V}{2} ρ_{o} g + \frac{V}{2} ρ_{w} g$

where, $ρ_{o} =$ density of oil.

$\Rightarrow 2 ρ_{b} = ρ_{o} + ρ_{w}$

$\begin{aligned} \Rightarrow & \frac{2 ρ_{b}}{ρ_{w}} & = \frac{ρ_{o}}{ρ_{w}} + 1 \\ \Rightarrow & 2 \times \frac{4}{5} & = \frac{ρ_{o}}{ρ_{w}} + 1 \\ \Rightarrow & ρ_{0} / ρ_{w} & = 8 / 5 - 1 \\ = 3 / 5 = 0.6 \end{aligned}$

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Properties of Matter 2 Question 2

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

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अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Properties of Matter 2 Question 2

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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