For an electric toothbrush is input energy equal to useful output energy ? Explain?

No. Refer to the three laws of thermodynamics. In layman's terms they are:

1. you don't get something for nothing.
2. you don't even get that much
3. absolute zero = zero entropy

For your question we refer to law 2 -- every system has inefficiency (due to friction, etc.). So output energy is always less than input energy. This is why perpetual motion machines do not work -- over time energy will be lost.
No, the input energy isn't equivalent to the output for an electric toothbrush. Some energy is lost as heat, for example.
NO! How could it be? No system is 100% efficient. There are always losses due to factors such as friction, heat, resistance.
No. Not if you define the useful output energy as the vibrating effect. Some of the input energy will be converted to heat, which has no useful effect (for the purposes of brushing teeth)
I agree with all the above answers, I also think some energy is lost as sound with that buzzzzzing you get
the law to which everyone is referring is the law of ethalpy, the Second Law of Thermodynamics. Basically this means that the electricity required to run the motor in your electric toothbrush is transferred into motion, but that some of this energy is converted into heat, and some of the energy is transferred to your hand and down your arm when you brush.
This refers to the efficiency of your electric toothbrush. So if 60% of the electricity requred to run your toothbrush actually went into the work of cleaning your teeth, the toothbrush would be 60% efficient (40% of the electricity was converted to heat/ vibration in your arm and didn't actually get used in cleaning your teeth)

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