Will the centripetal force on the bob be different on the moon

Hello
I think some details of the question are missing. However, I believe you are referring to a bob following some circular path. Therefore, the answer is "no": in fact, the centripetal force is equal on the earth and on the moon. 

Keep in mind that the centripetal force is given by

where m is the mass, v the tangential velocity and r the radius of the circular motion. The mass m of the bob is the same on the earth and on the moon, so the centripetal force is the same.