Question

The two pulley arrangements shown in the figure are
identical. The mass of the rope is negligible. In (a) the
mass m is lifted up by attaching a mass 2m to the other end
of the rope. In (b). m is lifted up by pulling the other end of
the rope with a constant downward force of 2mg. The
ratio of accelerations in two cases will be

Answer 1

Check it out since 2mg is the force applied, directly we can use formula f=ma and get the answer

Answer 2

Answer: a= g

Given:

mass 1 = 2m,

mass 2 =2mg

Solution:  

We know that, Force is a form of energy that contributes to movement of an object if applied. It can be expressed as below,

 F = ma

For (a),

T – mg = ma ⇒ (1)

2mg - T = 2ma ⇒ (2)

Substitute (1) in (2)

2mg – mg – ma = 2ma

mg = 3ma

⇒ a = g/3

for (b),

2mg is the force applied

Hence (2) becomes, 2mg = 2ma

⇒ a = g