Explanation:
A liquid drop has only one free surface, so its excess pressure is P = 2T/R. However, a soap bubble in the air has two completely free surfaces (an inner one and an outer one). Because both surfaces exert surface tension forces inward, the total excess pressure inside a soap bubble is exactly double: P = 4T/R.
Explanation:
Acceleration a = dv/dt ⇒ dv = a·dt. Integrating: ∫dv = ∫a·dt ⇒ Δv = area under a-t graph. Slope of v-t gives acceleration; area under a-t gives velocity change. Memory aid: 'a-t graph area = Δv; v-t graph area = displacement'. Graph interpretation skill essential for motion analysis in competitive exams.
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