why dosent a body dropped outside the lift experience any acceleration even though the lift is accelerating???

when a body is inside a lift then there can be two cases of a body experiencing any acceleration....

Ist Case:

when the body is resting on a platform of the elevator(lift) or is touching any walls of the elevator.....

then the body will experience three (minimum) kinds of forces i.e 1) Normal reaction 2) the weight Mg 3) and a pseudo force due to the acceleration of the lift 'a'

2nd Case :

the next case is when a body is not touching any platform(or wall) of the elevator then we will not need any kind of normal forces or pseudo forces to balance the equation because the body is now falling freely under the gravity 'g'.....

For Example: if a body is on a lift and the lift is accelerating downwards at a rate of 12 m/s² and we know that the value of g=10 m/s² therefore , now the body will get separated from the base of the platform as the lift's acceleration is greater than 'g' and so the body will now fall freely under the gravity....

And thus a body dropped outside a lift doesnt experience any acceleration(other than 'g') even though the lift is accelerating because it doesnt need to be equated with any normal force or any pseudo forces....

hope this helps.....;)