JEE Mains · Physics · STD 11 - Surface tension
- JEE Mains 2023
- Medium
- Numerical
A spherical drop of liquid splits into \(1000\) identical spherical drops. If \(u _{ i }\) is the surface energy of the original drop and \(u_f\) is the total surface energy of the resulting drops, the (ignoring evaporation). \(\frac{u_f}{u_i}=\left(\frac{10}{x}\right)\). Then value of \(x\) is \(......\)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(1\)
Step-by-step Solution
Detailed explanation
Surface Tension \(= T\)
\(R\) : Radius of bigger drop
\(r :\) Radius of smaller drop
Volume will remain same
\(\frac{4}{3} \pi R ^3=1000 \times \frac{4}{3} \pi r^3\)
\(R =10 r\)
\(u _{ i }= T \cdot 4 \pi R ^2\)
\(u _{ f }= T .4 \pi r ^2 \times 1000\)
\(\frac{ u _{ f }}{ u _{ i }}=\frac{1000 r ^2}{ R ^2}\)
\(\frac{ u _{ f }}{ u _{ i }}=\frac{10}{1}\)
So, \(x =1\)
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