Question

When an air bubble of radius r rises from the bottom to the surface of the water lake its radius becomes 5r/4. If the
temperature is constant and atmospheric pressure is 10 m of water column, the depth of the lake is approximately
(A)
3.3 m
(B)
5.3 m
(C)
9.53 m
(D)
6.5 m​

Answer 1

Answer:

Approximately=5.3meter will your answer , otherwise ask to google to get the answer....

Answer 2

Answer:9.5 m

Explanation:

Pressure at bottom  

(P  

1

​  

)=P  

atm

​  

+ρgh+  

R  

1

​  

 

4T

​  

__________(1)

Pressure at top

(P  

2

​  

)=P  

atm

​  

+  

R  

2

​  

 

4T

​  

____________(2)

Given R  

1

​  

=r

R  

2

​  

=  

4

5r

​  

 

So P  

1

​  

V  

1

​  

=P  

2

​  

V  

2

​  

 

(P  

1

​  

)  

3

4

​  

πr  

3

=(P  

2

​  

)  

3

4

​  

 

64

125r  

3

 

​  

 

Dividing (1) and (2)

P  

2

​  

 

P  

1

​  

 

​  

=  

P  

atm

​  

+  

5r

4T×4

​  

 

P  

atm

​  

+ρgh+  

r

4T

​  

 

​  

=  

64

125

​  

 

ρg(10)

ρg(10)+ρgh

​  

=  

64

125

​  

 

640+64h=1250

On solving we get h = 9.5 m