two soap bubbles have radii in the ratio 2:3. compare the excess of pressure inside these bubbles. also compare the works done in blowing these bubbles.
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Given :
Let R1 and R2 be the radii of two soap bubbles
R1/R2=2/3
let σ be the surface tension of soap bubble.
Excess pressure inside bubble with radius R1=P1=4σ/R1
Excess pressure inside bubble with radius R2=P2=4σ/R2
P1/P2=[4σ/R1 ]xR2/4σ
=R2/R1
=3/1
=1.5
Work done in blowing soap bubble of radius R1=W1=σ x 2x 4πR1²
Work done in blowing soap bubble of radius R2=W2=σ x 2x 4πR2²
W1/w2=σ x 2x 4πR1²/σ x 2x 4πR2²=(R1/R2)²=(2/3)²=4/9
∴Ratio of Workdone is 4:9
Let R1 and R2 be the radii of two soap bubbles
R1/R2=2/3
let σ be the surface tension of soap bubble.
Excess pressure inside bubble with radius R1=P1=4σ/R1
Excess pressure inside bubble with radius R2=P2=4σ/R2
P1/P2=[4σ/R1 ]xR2/4σ
=R2/R1
=3/1
=1.5
Work done in blowing soap bubble of radius R1=W1=σ x 2x 4πR1²
Work done in blowing soap bubble of radius R2=W2=σ x 2x 4πR2²
W1/w2=σ x 2x 4πR1²/σ x 2x 4πR2²=(R1/R2)²=(2/3)²=4/9
∴Ratio of Workdone is 4:9
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