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 the 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 $=2 \pi r^{2}$
$A _2=$ 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
Equate the net downward forces and net upward forces, we get, $h_1=\frac{5}{3} h$.
BETA
