Step 1: Understanding the Concept
For a second order reaction, rate \(=k[A]^2\).
Step 2: Double the concentration
The new rate \(=k(2[A])^2=4k[A]^2\).
Step 3: Compare
The rate becomes four times the original, so it quadruples, option (B).
Final Answer:
The rate becomes four times the initial rate.
\[ \boxed{\text{(B) }\text{It quadruples}} \]