in the image the big wheel will rotate small wheel connected to a generator the for is generated by pulley attached to shaft or small wheel fixed to big wheel and is lifted manually

i am not an expert that's why i need your help. Please consider it 12 grade or high school

to run an set of led bulb to light a small room for 24hrs using this gear motor what will be the weight needed

If you've taken high school physics you should know how to calculate this.

 

The amount of energy available to you is the gravitational potential energy of the mass, mgh. The amount of energy you need is the power consumed by the bulb multiplied by the time (86400 sec) LEDs run at around 2V and require maybe 10-20 mA of current, so lets call this 25 mW of power. You need 2160 joules of energy at a minimum. Let's be more realistic and assume 50% efficiency for the system. If you have 1 meter of space for the mass to drop, the mass needs to be 0.5*E/gh = 440 kg. Or 220 kg for a 2m drop. That's a tad much. Yo could dig a put and go for a 10m drop and get down to 44kg, but that's still a lot.

 

A real product that tries this is gravitylight http://gravitylight.org/ whose goal is less aggressive. If you look at their FAQ, from a 12.5 kg load: "The duration of the drop is 28min on low light, 20min on medium and 12min on high." They also have some specs listed, which are similar to my calculations