Step 1: Understand the process of starting the auto.
When the auto driver pulls the rope, they are providing mechanical energy to rotate a component in the system. This mechanical energy is converted into electrical energy to generate the initial current required to start the engine. The device responsible for this conversion is a dynamo.
Step 2: Analyze the options.
- (1) Battery: A battery stores electrical energy and does not convert mechanical energy into electrical energy. It provides power to the vehicle once the engine is running.
- (2) Transformer: A transformer is used to change the voltage levels of alternating current (AC) and does not convert mechanical energy into electrical energy.
- (3) Fuse: A fuse is a safety device that protects electrical circuits from excessive current. It does not convert energy from one form to another.
- (4) Dynamo: A dynamo is a device that converts mechanical energy into electrical energy through electromagnetic induction. This is the correct device used in this scenario.
Final Answer: The device used to convert mechanical energy to electrical energy is \( \mathbf{\text{dynamo}} \), which corresponds to option \( \mathbf{(4)} \).