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)
Show Answer
Answer:
Correct Answer: 11. (b)
Solution:
- 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, $h _1=\frac{5}{3} h$.
