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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 is

2. The length of the liquid column in the pipe is 

Asked by naresh230371 16th February 2018, 9:21 PM
Answered by Expert
Answer:
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

begin mathsize 12px style p cross times pi cross times 16 space equals space 3 cross times g plus pi cross times 1 cross times 1 cross times h cross times rho cross times g end style
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
 
begin mathsize 12px style p cross times pi cross times 15 space equals space 3 cross times g
h e n c e space p space equals space fraction numerator 3 cross times g over denominator pi cross times 15 end fraction space
a g a i n space p space equals space rho g h space equals space fraction numerator 3 cross times g over denominator pi cross times 15 end fraction
h e n c e space h space equals fraction numerator 3 over denominator pi cross times 15 cross times 1000 end fraction space
w e space g e t space h space equals space 0.064 space m m end style
 
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  
 
begin mathsize 12px style H space equals space fraction numerator 499 over denominator pi cross times 400 cross times 400 end fraction space equals space 10 space cross times space 10 to the power of negative 4 end exponent space c m space equals space 10 cross times space 10 to the power of negative 3 space end exponent m m end stylebegin mathsize 12px style H space equals space fraction numerator 499 over denominator pi cross times 400 cross times 400 end fraction space equals space 10 space cross times space 10 to the power of negative 4 end exponent space c m space equals space 10 cross times space 10 to the power of negative 3 space end exponent m m end style
hence piston will raise by 10 micro metre
Answered by Expert 19th February 2018, 2:45 PM
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