The amount of work done to break a big water drop of radiu 'R' into 27 small drops of equal radius is 10 J. The work done required to break the same big drop int 64 small drops of equal radius will be [2025]

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Solution

Q.
The amount of work done to break a big water drop of radius 'R' into 27 small drops of equal radius is 10 J. The work done required to break the same big drop into 64 small drops of equal radius will be [2025]

1 15 J

2 10 J

3 20 J

4 5 J

Ans.
(1)

The amount of work done to break a big water drop into small drops,

$W = △ U = T △ A$

One drop to n drops

$\frac{4}{3} π R^{3} = n \frac{4}{3} π r^{3} \Rightarrow r = \frac{R}{n^{\frac{1}{3}}}$

So, $W = T (n 4 π r^{2} - 4 π R^{2}) = T 4 π R^{2} (n^{1 / 3} - 1)$

For one drop to 27 drops

$W = T 4 π R^{2} (27^{1 / 3} - 1)$ ...(i)

For one drop to 64 drops

$W' = T 4 π R^{2} (64^{1 / 3} - 1)$ ...(ii)

(ii)/(i)

$\frac{W'}{W} = \frac{4 - 1}{3 - 1} = \frac{3}{2} \Rightarrow W' = \frac{3}{2} W = 15 J$

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