Adding root value to a response from has_many_through relationship

Question

I have a has_many through relationship in rails app. I is associated as follows:

 class Car < ActiveRecord::Base
     has_many :car_fuel_types
     has_many :fuel_types , through: :car_fuel_types 
 end

class FuelType < ActiveRecord::Base
     has_many :car_fuel_types
     has_many :cars , through: :car_fuel_types
end

class CarFuelType < ActiveRecord::Base
    belongs_to :fuel_type
    belongs_to :car
end

In my cars_controller I want to get all to get all the Cars with a particular fuel_type, so I am writing the following logic in my cars_controller index action

def index    
    @cars = FuelType.find(params[:fuel_type_id]).cars
end

And I am using this curl command to test the result

curl -i -H "Accept: application/json" -H "Content-type: application/json"  -X GET http://localhost:3000/cars.json\?fuel_type_id\=2

So this is giving me the list of cars with the selected fuel_type.

Now I want to add root to "cars" to the json response that I am getting, while trying to do that I came across active_model_serializers gem and read that I have to add the render block in my controller index aciton

So my new controller looks like:

def index    
    @cars = FuelType.find(params[:fuel_type_id]).cars
    respond_to do |format|
       format.html
       format.json { render json: @cars }
    end
end

hen I do this and try to the same curl command, it is giving me error in the render json :cars line.

The error that I am getting is:

 NoMethodError - undefined method `fuel_type_id' for #<Car:0x007f36ff104a18>:

Can anyone tell me what should I do so that I get a root element in my response ?