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 :
![](https://imagex.cdn.examgoal.net/jgy2xukflzmqnh/b707c534-7cc5-4a9a-b5f8-d820e0304e4a/e08c51d0-013c-11eb-8293-3b6cc591631c/file-jgy2xukflzmqni-331w.png)

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

Choose the correct answer: