Peculiar Acceleration: Solving a Massless and Frictionless Pulley Problem

[Vibhor]

Homework Statement

All pulleys are massless and frictionless and string is massless . Find the acceleration of the two masses and the two pulleys .

Homework Equations

The Attempt at a Solution

I will call the left mass A and right mass B and left pulley P and right pulley R .

Acceleration of B is same as pulley R .

From the string constraint , the relationship between accelerations is $a_P = a_A+2a_B$

Consider the forces on pulley P . Since it is massless , tension in the string has to be 0 .

Since tension is zero , accelerations of both A and B is $g$ downwards .

Acceleration of pulley P comes out to be $3g$ downwards .

The results look quite strange , especially the acceleration of left pulley .

How is left pulley P accelerating downwards with acceleration greater than g ?

Cam someone point out the mistake .

Many thanks

 

[haruspex]

How is left pulley P accelerating downwards with acceleration greater than g ?

I don't see why it should not. Even if it had mass, it would be possible to construct a pulley arrangement with other, larger masses that would make it drop faster than g.

 

[Vibhor]

I don't see why it should not. Even if it had mass, it would be possible to construct a pulley arrangement with other, larger masses that would make it drop faster than g.

OK. So the result that acceleration of pulley P is $3g$ downwards is correct ?

 

[haruspex]

OK. So the result that acceleration of pulley P is $3g$ downwards is correct ?

Your reasoning all looks right to me.