SATHEE: Properties of Matter 2 Question 11

Properties of Matter 2 Question 11

11. Now level of the liquid starts decreasing slowly. When the level of liquid is at a height $h_{1}$ above the cylinder the block starts moving up. At what value of $h_{1}$ , will the block rise?

(a) $4 h / 9$

(b) $5 h / 9$

(c) $5 h / 3$

(d) Remains same

$(2006, 5$ M)

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Answer:

Correct Answer: 11. (b)

Solution:

Let $A_{1} =$ Area of cross-section of cylinder $= 4 π r^{2}$

$A_{2} =$ Area of base of cylinder in air $= π r^{2}$

and $A_{3} =$ Area of base of cylinder in water

$= A_{1} - A_{2} = 3 π r^{2}$

Drawing free body diagram of cylinder

Equating the net downward forces and net upward forces, we get, $h_{1} = \frac{5}{3} h$ .

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Properties of Matter 2 Question 11

11. Now level of the liquid starts decreasing slowly. When the level of liquid is at a height h1 above the cylinder the block starts moving up. At what value of h1, will the block rise?

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11. Now level of the liquid starts decreasing slowly. When the level of liquid is at a height $h_{1}$ above the cylinder the block starts moving up. At what value of $h_{1}$ , will the block rise?