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A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be
- a)4 cm
- b)8 cm
- c)10 cm
- d)20 cm
Correct answer is option 'B'. Can you explain this answer?
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A 20 cm long capillary tube is dipped in water. The water rises up to ...
Given: Length of capillary tube = 20 cm, Height of water column in the capillary tube = 8 cm
To find: Length of water column in the capillary tube in a freely falling elevator
Explanation:
In a freely falling elevator, the acceleration of the elevator is equal to the acceleration due to gravity (g). This means that the apparent weight of the body inside the elevator becomes zero. In this situation, the pressure inside the liquid column in the capillary tube changes due to the weight of the liquid column. This change in pressure causes the liquid column to rise or fall in the capillary tube.
According to the law of capillarity, the height (h) of the liquid column in a capillary tube is given by the formula:
h = 2T cosθ/ρgr
where T is the surface tension of the liquid, θ is the angle of contact, ρ is the density of the liquid, g is the acceleration due to gravity, and r is the radius of the capillary tube.
Since the length of the capillary tube and the radius are constant, the height of the liquid column depends only on the surface tension, density, and the angle of contact of the liquid.
In this case, the length of the capillary tube and the radius are constant, and the surface tension and density of water are also constant. Therefore, the height of the water column in the capillary tube will remain the same in the freely falling elevator.
Therefore, the length of the water column in the capillary tube will be 8 cm, which is the same as the original height of the water column in the capillary tube.
Hence, the correct option is (b) 8 cm.
To find: Length of water column in the capillary tube in a freely falling elevator
Explanation:
In a freely falling elevator, the acceleration of the elevator is equal to the acceleration due to gravity (g). This means that the apparent weight of the body inside the elevator becomes zero. In this situation, the pressure inside the liquid column in the capillary tube changes due to the weight of the liquid column. This change in pressure causes the liquid column to rise or fall in the capillary tube.
According to the law of capillarity, the height (h) of the liquid column in a capillary tube is given by the formula:
h = 2T cosθ/ρgr
where T is the surface tension of the liquid, θ is the angle of contact, ρ is the density of the liquid, g is the acceleration due to gravity, and r is the radius of the capillary tube.
Since the length of the capillary tube and the radius are constant, the height of the liquid column depends only on the surface tension, density, and the angle of contact of the liquid.
In this case, the length of the capillary tube and the radius are constant, and the surface tension and density of water are also constant. Therefore, the height of the water column in the capillary tube will remain the same in the freely falling elevator.
Therefore, the length of the water column in the capillary tube will be 8 cm, which is the same as the original height of the water column in the capillary tube.
Hence, the correct option is (b) 8 cm.
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A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will bea)4 cmb)8 cmc)10 cmd)20 cmCorrect answer is option 'B'. Can you explain this answer?
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