An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury level. The open end of the tube is then chosen and scaled and the tube raised vertically up by an additional 46 cm. What will be the length of the air column above the mercury in the tube now? (Atmospheric pressure = 76 cm of Hg)
1. 38 cm
2. 6 cm
3. 16 cm
4. 22 cm
There is a circular tube in a vertical plane. Two liquids that do not mix and of densities and are filled in the tube. Each liquid subtends angle at the centre. Radius joining their interface makes an angle with the vertical. Ratio is:
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On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be the spheres of radius R and making a circular contact of radius r with the bottom of
the vessel. If r << R and the surface tension of water is T, the value of r just before the bubbles detach is : (density of water is )
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In materials like aluminum and copper, the correct order of magnitude of various elastic moduli is :
1. Young's moduli < Shear moduli < Bulk moduli
2. Bulk moduli < Shear moduli < Young's moduli
3. Shear moduli < Young's moduli < Bulk moduli.
4. Bulk moduli < Young's moduli < Shear moduli
A capillary tube is immersed vertically in the water and the height of the water column is x. When this arrangement is taken into a mine of depth d, the height of the water column is y. If R is the radius of the earth, the ratio x/y is :
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Two tubes of radii respectively, are connected in series and a liquid flows through each of them in streamline conditions. are pressure differences across the two tubes. If will be equal to :
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A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity 0.8). The height of the water is 3 m and that of kerosene is 2 m. When the hole is opened, the velocity of fluid coming out from it is near: (take g = 10 and density of water = )
1. 10.7
2. 9.6
3. 8.5
4. 7.6
When an air bubble of radius r rises from the bottom to the surface of the lake, its radius becomes . Taking the atmospheric pressure to be equal to 10 m height of water column, the depth of the lake would approximately be (ignore the surface tension and the effect of temperature) :
1. 11.2 m
2. 8.7 m
3. 9.5 m
4. 10.5 m
An air bubble of radius 0.1 cm is in a liquid having surface tension 0.06 N/m and density . The pressure inside the bubble is 1100 greater than the atmospheric pressure. At what depth is the bubble below the surface of the liquid? (g = 9.8 )
1. 0.1 m
2. 0.15m
3. 0.20 m
4. 0.25 m
A small soap bubble of radius 4 cm is trapped inside another bubble of radius 6 cm without any contact. Let be the pressure inside the inner bubble and be the pressure outside the outer bubble. The radius of another bubble with the pressure difference between its inside and outside would be :
1. 12 cm
2. 2.4 cm
3. 6 cm
4. 4.8 cm
A cylindrical vessel of cross-section A contains water to a height h. There is a hole in the bottom of the radius 'a'. The time in which it will be emptied is :
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A ball of density and radius r is dropped on the surface of a liquid of density from certain height. If the speed of ball does not change even on entering in liquid and viscosity of the liquid is , then the height from which the ball dropped is :
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Two soap bubbles coalesce to form a single bubble. If V is the subsequent change in volume of contained air and S the change in total surface area, T is the surface tension and P atmospheric pressure, which of the following relation is correct?
1. 4PV + 3ST = 0
2. 3PV + 4ST = 0
3. 2PV + 3ST = 0
4. 3PV + 2ST = 0
The velocity of water in a river is 18 km/hr near the surface. If the river is 5 m deep, find the shearing stress between the horizontal layers of water. The coefficient of viscosity of water = poise.
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In the diagram shown in the figure, the difference in two tubes of the manometer is 5 cm, the cross-section of the tube at A and B is 6 mm and 10 mm respectively. The rate at which the water flows through the tube is (g =10 ).
1. 7.5 cc/s
2. 8.0 cc/s
3. 10.0 cc/s
4. 12.5 cc/s
A large number of liquid drops, each of radius r, coalesce to form a single drop of radius R. The energy released in the process is converted into kinetic energy of a big drop so formed. The speed of the drop is (given surface tension of the liquid is T, density is ).
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If it takes 5 mins to fill a 15-liter bucket from a water tap of diameter cm, then the Reynolds number for the flow is (density of water = and viscosity of water = ) close to:
1. 5500
2. 11,000
3. 550
4. 1100
If two glass plates have water between them and are separated by a small distance, it is very difficult to pull them apart. It is because of the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to the atmosphere. If the radius of the cylindrical surface is R and the surface tension of water is T, then the pressure in water between the plates is lower by :
1. T/4R
2. T/2R
3. T/R
4. 2T/R
A cylindrical block of wood (density = 650 kg ), of base area 30 and height 54 cm, floats in a liquid of density 900 kg The block is depressed slightly then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length (nearly):
1. 65 cm
2. 52 cm
3. 39 cm
4. 26 cm
Consider a water jar of radius R that has water filled up to height H and is kept on a stand of height h. Through a hole of radius r (r<< R) at its bottom, the water leaks out and the stream of water coming down the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of the water stream when it hits the ground is x. Then:
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