MHT CET · Physics · Mechanical Properties of Fluids
When a mercury drop of radius 'R', breaks into 'n' droplets of equal size, the radius 'r' of each droplet is
- A \(\mathrm{r}=\frac{\mathrm{R}}{\sqrt{\mathrm{n}}}\)
- B \(\mathrm{r}=\frac{\mathrm{R}}{\mathrm{n}}\)
- C \(\mathrm{r}=\frac{\mathrm{R}}{\mathrm{n}^{\frac{1}{3}}}\)
- D \(\mathrm{r}=\mathrm{R} \mathrm{n}^{\frac{1}{3}}\)
Answer & Solution
Correct Answer
(C) \(\mathrm{r}=\frac{\mathrm{R}}{\mathrm{n}^{\frac{1}{3}}}\)
Step-by-step Solution
Detailed explanation
Volume remains constant
\(\therefore \mathrm{n} \times \frac{4}{3} \pi \mathrm{r}^{3}=\frac{4}{3} \pi \mathrm{R}^{3}\)
\(\therefore \mathrm{nr}^{3}=\mathrm{R}^{3}\)
\(\therefore \quad n^{\frac{1}{3}} r=R \quad \therefore r=\frac{R}{n^{\frac{1}{3}}}\)
\(\therefore \mathrm{n} \times \frac{4}{3} \pi \mathrm{r}^{3}=\frac{4}{3} \pi \mathrm{R}^{3}\)
\(\therefore \mathrm{nr}^{3}=\mathrm{R}^{3}\)
\(\therefore \quad n^{\frac{1}{3}} r=R \quad \therefore r=\frac{R}{n^{\frac{1}{3}}}\)
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