Advertisements
Advertisements
प्रश्न
A wire forming a loop is dipped into soap solution and taken out so that a film of soap solution is formed. A loop of 6.28 cm long thread is gently put on the film and the film is pricked with a needle inside the loop. The thread loop takes the shape of a circle. Find the tension the the thread. Surface tension of soap solution = 0.030 N m−1.
Advertisements
उत्तर
The loop will take circular shape after pricking. Raduis of which is given by the relation.
Given:
Length of thread loop L = 6.28 cm
= 0.0628 m
Surface tension Ts = 0.030 N/m
Formula:
L = 2πr
r = `L/(2π)`
Solution:
`l = 2piR`
`R = l/(2pi)`
= `0.0628/ (2 xx 3.14)`
= `(0.0628)/ (6.28)`
= 0.01 m
= 10−2 m
∴ R = 10−2 m
2T sin dθ force in inward direction is balanced by the surface tension force in the outward direction.
∴ 2T sin(θ) = (surface tension ) × (length of are )
For small angles,
sin d(θ) = d(θ)
∴ 2Td(θ) = S(2Rdθ) ...(S = Surface tension)
∴ T = SR
= 10−2 × 0.030
= 3.0 × 10−4 N
APPEARS IN
संबंधित प्रश्न
Explain why Water on a clean glass surface tends to spread out while mercury on the same surface tends to form drops. (Put differently, water wets glass while mercury does not.)
When the size of a soap bubble is increased by pushing more air in it, the surface area increases. Does it mean that the average separation between the surface molecules is increased?
If more air is pushed in a soap bubble, the pressure in it
A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be
A drop of mercury of radius 2 mm is split into 8 identical droplets. Find the increase in surface energy. Surface tension of mercury = 0.465 J m−2.
Insect moves over the surface of water because of ______.
Numerical Problem.
A stone weighs 500 N. Calculate the pressure exerted by it if it makes contact with a surface of area 25 cm2.
How does surface tension help a plant?
Distinguish between cohesive and adhesive forces.
What are the factors affecting the surface tension of a liquid?
A drop of oil placed on the surface of water spreads out. But a drop of water place on oil contracts to a spherical shape. Why?
What is capillarity?
Two small drops of mercury each of radius 'R' coalesce to form a large single drop. The ratio of the total surface energies before and after the change is ____________.
Two spherical rain drops reach the surface of the earth with terminal velocities having ratio 16 : 9. The ratio of their surface area is ______.
A water drop of radius R' splits into 'n' smaller drops, each of radius 'r'. The work done in the process is ______.
T = surface tension of water
The length of a needle floating on water is 2 cm. The additional force due to surface tension required to pull the needle out of water will be (S.T. of water = 7.0 × 10−2 N/m).
The free surface of oil in a tanker, at rest, is horizontal. If the tanker starts accelerating the free surface will be titled by an angle θ. If the acceleration is a ms–2, what will be the slope of the free surface?
Two mercury droplets of radii 0.1 cm. and 0.2 cm. collapse into one single drop. What amount of energy is released? The surface tension of mercury T = 435.5 × 10–3 Nm–1.
When an air bubble of radius r rises from the bottom to the surface of a lake, its radius becomes `(5r)/4`. Taking the atmospheric pressure to be equal to the 10 m height of the water column, the depth of the lake would approximately be ______.
(ignore the surface tension and the effect of temperature)
A light metal disc of radius ‘r’ floats on water surface and bends the surface downwards along the perimeter making an angle ‘θ’ with the vertical edge of the disc. If the weight of water displaced by the disc is ‘W’, the weight of the metal disc is ______.
[T = surface tension of water]
