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 static pressure d is the density of water and E is the total energy of explosion. Find the value of a,b and c.

Explanation

To solve the problem, we need to find the values of \( a \), \( b \), and \( c \) in the expression \( T \propto p^a d^b E^c \), where \( p \) is static pressure, \( d \) is the density of water, and \( E \) is the total energy of the explosion. We will use dimensional analysis to achieve this.

### Step 1: Write down the dimensions of each variable.
1. **Pressure \( p \)**:
- Pressure is defined as force per unit area.
- The dimensional formula for force is \( [F] = M L T^{-2} \).
- The dimensional formula for area is \( [A] = L^2 \).
- Therefore, the dimensional formula for pressure is:
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