Properties Of Matter Ques 50
Passage Based Questions
A wooden cylinder of diameter $4 r$, height $h$ and density $\rho / 3$ is kept on a hole of diameter $2 r$ of tank, filled with liquid of density $\rho$ as shown in the figure.
- 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: 50.(c)
Solution:
Formula:
- 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, $h _1=\frac{5}{3} h$.
BETA
