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Question
The energy stored in a soap bubble of diameter 6 cm and T = 0.04 N/m is nearly ______.
Options
0.9 × 10–3J
0.4 × 10–3J
0.7 × 10–3J
0.5 × 10–3J
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Solution
The energy stored in a soap bubble of diameter 6 cm and T = 0.04 N/m is nearly 0.9 × 10–3J
Explanation:
Increase in surface area of the sphere is given by:
A = `4pir^2` ......(i)
Here, r is the radius of the sphere and A is the increase in the surface area.
The bubble contains two surfaces. So multiply Equation (i) by 2
A = `2 xx 4pir^2` .....(ii)
Diameter = 6 cm i.e. r = 3 cm
Substitute the value of r = 3 cm to find the value of the area.
A = `2 xx 4pi xx (3 " cm" xx (1" m")/(100 " cm"))^2`
A = 0.023 m2
The formula for stored energy is:
E = T × A
Here, T is the surface tension.
Substitute the value of T = 0.04 N/m and A = 0.023 m2 to find the stored energy.
E = T × A
E = 0.04 N/m × 0.023 m2
E = 0.9 × 10–3J
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