A vessel whose bottom has a round hole with diameter 0.1 mm is filled with water. the maximum height up to which water can be filled without leakage is ___ cm (given surface tension =7.5×10−2nm−1 and g=10ms−2)
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Answered by
62
∵ surface tension is given by
T = hrdg/2
Here, h is height of liquid
r is the radius of hole
d is density of liquid
g is Acceleration due to gravity.
Given,
T = 7.5 × 10⁻² N/m = 0.075 N/m
r = 0.1 × 10⁻³/2 = 0.05 × 10⁻³ m
d = 10³ g/cm³ [ because liquid is water
g = 10 m/s²
∴ 0.075 = h × 0.05 × 10⁻³ × 10³ × 10/2
h = 0.075/0.25 = 3/10 m = 30 cm
Hence, height of water = 30 cm
T = hrdg/2
Here, h is height of liquid
r is the radius of hole
d is density of liquid
g is Acceleration due to gravity.
Given,
T = 7.5 × 10⁻² N/m = 0.075 N/m
r = 0.1 × 10⁻³/2 = 0.05 × 10⁻³ m
d = 10³ g/cm³ [ because liquid is water
g = 10 m/s²
∴ 0.075 = h × 0.05 × 10⁻³ × 10³ × 10/2
h = 0.075/0.25 = 3/10 m = 30 cm
Hence, height of water = 30 cm
Answered by
26
Surface Tension T = hrdg/ 2
where
Surface Tension =T = 7.5×10⁻² N/m
radius=r = 0.1 × 10⁻³/2 = 0.05 × 10⁻³ m
density of liquid = water=d = 10³/m3
g=10m/s2
Now height h= 2T/rdg
h=2×7.5×10⁻²/ (0.05 × 10⁻³ m )x10³×10
h=2×7.5×10⁻³ /0.05
=0.3m
h= 30cm
Therefore height up to which water can be filled up without leakage is 30cm
where
Surface Tension =T = 7.5×10⁻² N/m
radius=r = 0.1 × 10⁻³/2 = 0.05 × 10⁻³ m
density of liquid = water=d = 10³/m3
g=10m/s2
Now height h= 2T/rdg
h=2×7.5×10⁻²/ (0.05 × 10⁻³ m )x10³×10
h=2×7.5×10⁻³ /0.05
=0.3m
h= 30cm
Therefore height up to which water can be filled up without leakage is 30cm
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