Final answer:
To calculate the energy needed to break a water drop into 1 million droplets considering surface tension, we compare the initial and final surface areas multiplied by the surface tension, leading to the answer of (c) 100s is correct.
Step-by-step explanation:
The question asks us to calculate the energy required to break a water drop into many smaller droplets, considering the surface tension of water. Surface tension is the energy needed to increase the surface area of a liquid. The total energy change is the difference between the energies of the initial and final configurations of the droplets.
To solve the problem, we need to know that surface energy can be calculated using the formula:
E = s × A
where E is the energy, s is the surface tension, and A is the surface area. For a sphere, the surface area is given by:
A = 4πr²
For the initial drop, the radius is 1 mm, and for the final droplets, each radius would be much smaller since the volume is conserved and we have 1 million smaller droplets.
By comparing the initial and final surface areas and multiplying by the surface tension, we find that the energy required to break the drop into smaller droplets is c) 100s.