What will be the duration of the day, if the earth suddenly shrinks to `1//64 th` of its original volume, mass remaining unchenged ?

Explanation

To solve the problem of determining the duration of a day if the Earth suddenly shrinks to \( \frac{1}{64} \) of its original volume while keeping its mass unchanged, we can follow these steps:

### Step 1: Understand the relationship between volume and radius
The volume \( V \) of a sphere is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]
If the volume of the Earth shrinks to \( \frac{1}{64} \) of its original volume, we can express this as:
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