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Physics Question 18 – NEET-UG 2023

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The amount of energy required to form a soap bubble of radius 2 cm from a soap solution is nearly : (surface tension of soap solution =0.03 N m−1)

The energy required to form a soap bubble is equal to the work done against surface tension, which is stored as potential energy in the increased surface area.

🥷
Ninja Strategy•Magnitude Estimation

Perform a quick order-of-magnitude calculation using approximate values for π and the given numbers to eliminate options that are clearly too large or too small.

Step 1: Identify Given Values and Formula✦ Active

The radius of the soap bubble is r=2 cm=0.02 m. The surface tension of the soap solution is T=0.03 N m−1. The energy required to form a soap bubble is the work done against surface tension, given by W=T×ΔA, where ΔA is the total change in surface area.

💡 Teacher's Secret Hint

Always convert units to SI (meters, Newtons) before calculation to avoid errors.

Step 2: Calculate the Total Surface Area○ Expand

A soap bubble has two free surfaces (an inner and an outer surface). Therefore, the total surface area of a soap bubble of radius r is twice the surface area of a single sphere.

ΔA=2×(4πr2)=8πr2

Substitute the value of r:

ΔA=8π(0.02 m)2=8π(0.0004 m2)=0.0032π m2
💡 Teacher's Secret Hint

A common mistake is to forget the factor of 2 for a soap bubble (which has two surfaces) versus a liquid drop (which has one surface).

Step 3: Calculate the Energy Required○ Expand

Now, substitute the values of T and ΔA into the work done formula:

W=T×ΔA=(0.03 N m−1)×(0.0032π m2) W=0.000096π J

Using π≈3.14159:

W=0.000096×3.14159 J≈0.00030159 J W≈3.016×10−4 J

Comparing this value with the given options, option (3) is the closest.

💡 Teacher's Secret Hint

Pay attention to the powers of 10 in the options and your calculated result.

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