The correct option is D.
Lumen is used to quantify the amount of total light energy that a source is putting out in all direction, thus, it refers to luminous output of a light source. Initial lumen refers to the luminosity of a light when it was first turned on; the luminosity is highest at this point.
The power dissipated across a component can be calculated through the formula P=I^2xR
Substituting the values in we get P=(0.5)^2x10=2.5W
Mechanical energy (ME) is the sum of potential energy (PE) and kinetic energy (KE). When the toy falls, energy is converted from PE to KE, but by conservation of energy, ME (and therefore PE+KE) will remain the same.
Therefore, ME at 0.500 m is the same as ME at 0.830 m (the starting point). It's easier to calculate ME at the starting point because its just PE we need to worry about (but if we wanted to we could calculate the instantaneous PE and KE at 0.500 m too and add them to get the same answer).
At the start:
ME = PE = mgh
ME = 0.900 (9.8) (0.830)
ME = 7.32 J
