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. (c)

Solution:

  1. Let $A _1=$ Area of cross-section of cylinder $=4 \pi r^{2}$

$A _2=$ Area of base of cylinder in air $=\pi r^{2}$

and $A _3=$ Area of base of cylinder in water

$$ =A _1-A _2=3 \pi r^{2} $$

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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