If the time period `(T)`of vibration of a liquid drop depends on surface tension `(S)` , radius`( r )` of the drop , and density `( rho )` of the liquid , then find the expression of `T`.

Explanation

To find the expression for the time period \( T \) of vibration of a liquid drop that depends on surface tension \( S \), radius \( r \), and density \( \rho \), we can use dimensional analysis. Here are the steps to derive the expression:

### Step 1: Assume the relationship
Assume that the time period \( T \) is proportional to the variables \( S \), \( r \), and \( \rho \):
\[ T \propto S^a r^b \rho^c \]
where \( a \), \( b \), and \( c \) are the powers to be determined.
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