That's the "angular frequency" or rotation "rate" of the motion.
“When the circuit is switched on, chemical (stored) energy in the battery is changed into electrical energy in wires and then into light and heat energy by bulb”
Find the final velocity of the rock first:
The total energy of the rock at rest:

The total energy of the rock after 7m:

Energy must be conserved:

Momentum must be conserved also.
Momentum with the ball at rest:

The total momentum is zero with the ball at rest and must remain zero.
Momentum with the ball at 7m:

Solving for the earth's velocity v₂: