Which statement is FALSE?

a) planetary nebulae can have layers because of pulsating stars
b) planetary nebulae usually last tens of thousands of years
c) a planetary nebula will be part of the end state of the Sun
d) planetary nebulae usually have black holes at their centers
e) planetary nebulae are a few light years in size

Two masses are connected by a rope that hangs over a pulley as shown below. the pulley is a uniform cylinder of radius 푅=0.381meters and mass 푀=3.1푘푔. initially 푚"is on the ground and 푚#rests 2.5 meters above the ground. if the system is released, use conservation of energy to determine the speed of 푚#just before it strikes the ground. assume the pulley bearing is frictionless.