A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5 10^-2 N/m. The pressure inside the bubble equals at a point Z_0 below the free surface of wate…

Question

A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5 10^-2 N/m. The pressure inside the bubble equals at a point Z_0 below the free surface of water in a container. Taking g=10 m/s^2, density of water =10^3 kg/m^3, the value of Z_0 is [NEET 2019]

Accepted Answer

Correct answer: B. (b) Given, surface tension T=2.5 10^-2 N/m , =10^3 kg/m^3 ,g=10 ms^-2 andr=1 mm=1 10^-3 m Let p_0 be the outside pressure from the water, then total pressure inside the bubble becomes p_1=p_0+ 4Tr …(i) The pressure at the depth Z_0 below the water surface is p_2=p_0+Z_0 ρg …(ii) As it is given that the pressure inside the bubble is same as the pressure at depth Z_0, then equating Eqs. (i) and (ii), we get p_0+ 4Tr=p_0+Z_0 g ⇒Z_0= 4T rpg … . ( iii ) Substituting these values in Eq. (iii), we get ⇒Z_0= 4 2.5 10^-21 10^-3 10^3 10=10 10^-3 m=1 cm

Solution

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