A gas bubble from an explosion under water oscillates with a period `T` proportional to `P^(a) d^(b) E^(c )`, where `P` is the pressure, `d` is density of water and `E` is the total energy of the explosion. Find the value of a,b and c`.

Explanation

To solve the problem, we need to determine the values of \(a\), \(b\), and \(c\) in the proportional relationship \( T \propto P^a d^b E^c \). We will use dimensional analysis to find these values.

### Step-by-Step Solution:

1. **Identify the dimensions of each quantity:**

- **Time period \(T\):**
\[
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