Question #86931

Question

Question #86931

1 Answer

Impact of this question

2917 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-22T11:43:27

When the hollow sphere with a small hole is immersed in water a thin film of water is formed at the mouth of the hole.This film acts as a membrane and prevents water to enter in the hollow sphere.

With increase in depth of immersion the pressure on this film goes to increase and slowly it acquires spherical shape and when a spherical droplet of diameter equal to the diameter of the hole is formed, water starts to enter into the cavity of hollow sphere. At this moment the excess pressure within the the spherical droplet of water becomes equal to the hyodrostatic pressure of water column at the depth of water that hole reaches.

The extra pressure within the droplet due to surface tension $P_{st} = \frac{2 γ}{r}$ $P_"st"=(2gamma)/r$
Where
$γ \to surface tension of water = 0.07 \frac{N}{m}$ $gamma->"surface tension of water"=0.07N/m$

$= \frac{0.07 \times 10^{5} dyne}{100 c m} = 70 dyne/cm$ $=(0.07xx10^5 "dyne")/(100cm)=70"dyne/cm"$

$r \to radius of the hole = ?$ $r->"radius of the hole"=?$

The hydrostatic pressure at h depth of water

$P_{hy} = h \times d \times g$ $P_"hy"=hxx d xxg$

where
$h \to depth of water = 40 c m$ $h->"depth of water"=40cm$

$d \to density of water = 1 g c m^{- 3}$ $d->"density of water"=1gcm^-3$

$g \to acceleration due to gravity = 980 c m s^{- 2}$ $g->"acceleration due to gravity"=980cms^-2$

By the condition

$P_{st} = P_{hy}$ $P_"st"=P_"hy"$

$\Rightarrow \frac{2 γ}{r} = h \times d \times g$ $=>(2gamma)/r=hxxd xxg$

$\Rightarrow r = \frac{2 γ}{h \times d \times g}$ $=>r=(2gamma)/(hxxd xxg)$

$\Rightarrow r = \frac{2 \times 70}{40 \times 1 \times 980} c m \approx 3.57 \times 10^{- 3} c m$ $=>r=(2xx70)/(40xx1 xx980)cm~~3.57xx10^-3cm$

So diameter of the hole $= 2 \times r = 7.14 \times 10^{- 3} c m$ $=2xxr=7.14xx10^-3cm$

Science

Math

Humanities

... and beyond

Question #86931

1 Answer

Related questions

Impact of this question