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# A piston weighing3 kg has the form of a circular disc of radius R=4 m. The disc has a hole into which a thin walled pipe of radius 1 m is inserted.initially the piston is at the bottom of the cylinder. Now 700 g of water is poured into the pipe.1. The height to which the piston will rise is2. The length of the liquid column in the pipe is

Asked by naresh230371 16th February 2018, 9:21 PM
Let us assume after pouring water, piston has raised and there is a water column in the pipe as shown in figure.
Let p be the pressure just below the piston bottom and let us consider three points A, B and C at same level which are at pressure p.

The pressure p is due to weight of the piston and weight of water column in the pipe above A. Since pressure = force×Area we can write

where ρ is density of water and h is height of water column in the tube above A

since ρgh = pressure p, we can write

The length of liquid column in the pipe is 0.064 mm

now if we calculate volume of liquid in the pipe above A as π × 100 × 100 × 0.0064 cm3 = 201 cm

hence remaining volume 499 cm3 is under piston

hence height of water column below piston is

π × 400 × 400 × H = 499 cm3

hence piston will raise by 10 micro metre
Answered by Expert 19th February 2018, 2:45 PM
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Tags: pressure