Question 432: Properties of Matter

Question

An open-ended U-tube of uniform cross-sectional area contains water (density 10
3
kg m
−3
). Initially the
water level stands at 0.29 m from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of
density 800 kg m
−3
is added to the left arm until its length is 0.1 m, as shown in the schematic figure
below. The ratio $$\left( {{{{h_1}} \over {{h_2}}}} \right)$$ of the heights of the liquid in the two arms is :

Accepted Answer

We have, h
1
+ h
2
= 0.29 $$ 	imes $$ 2 + 0.1
h
1
+ h
2
= 0.68 .......(i)
$$ \Rightarrow $$ p
0
+ $$ho $$
k
g(0.1) +$$ho $$
w
g(h
1
$$-$$ 0.1) $$-$$ $$ho $$
w
gh
2
= p
0
where, $$ho $$
k
= density of kerosene and $$ho $$
w
= density of water.
$$ \Rightarrow $$ $$ho $$
k
g(0.1) + $$ho $$
w
gh
1
$$-$$ $$ho $$
w
g $$ 	imes $$ (0.1) = $$ho $$
w
gh
2
$$ \Rightarrow $$ 800 $$ 	imes $$ 10 $$ 	imes $$ 0.1 + 1000 $$ 	imes $$ 10 $$ 	imes $$ h
1
$$-$$ 1000 $$ 	imes $$ 10 $$ 	imes $$ 0.1 = 1000 $$ 	imes $$ 10 $$ 	imes $$ h
2
$$ \Rightarrow $$ 10000(h
1
$$-$$ h
2
) = 200
$$ \Rightarrow $$ h
1
$$-$$ h
2
= 0.01 .......(ii)
Solving Eqs. (i) and (ii), we get
h
1
= 0.35
and h
2
= 0.33
So, $${{{h_1}} \over {{h_2}}} = {{35} \over {33}}$$

Answer

$${{15} \over {14}}$$

Answer

$${{35} \over {33}}$$

Answer

$${7 \over 6}$$

Answer

$${5 \over 4}$$

Properties of Matter

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