Answer:
The mass of the block, M =T/(3a +g) Kg
Explanation:
Given,
The upward acceleration of the block a = 3a
The constant force acting on the block, F₀ = Ma = 3Ma
The mass of the block, M = ?
In an Atwood's machine, the upward force of the block is given by the relation
Ma = T - Mg
M x 3a = T - Ma
3Ma + Mg = T
M = T/(3a +g) Kg
Where 'T' is the tension of the string.
Hence, the mass of the block in Atwood's machine is, M = T/(3a +g) Kg
To solve this problem we will apply the concepts related to the moment of inertia and Torque, the latter both its translational and rotational expression.
According to the information given the moment of inertia of the body would be

Replacing we have


Now the translational torque would be the product between the force applied (Its own Weight) and the distance (Its center of mass at the middle)




Now the rotational torque is defined as the product between the moment of inertia and the angular acceleration, then,

Replacing,


Therefore the angular acceleration is 
Displacement = velocity * time
Just substitute the value, & solve the equation.
Hope this helps!
Answer:
The ball experiences the greater momentum change
Explanation:
The momentum change of each object is given by:

where
m is the mass of the object
v is the final velocity
u is the initial velocity
Both objects have same mass m and same initial velocity u. So we have:
- For the ball, the final velocity is

Since it bounces back (so, opposite direction --> negative sign) with same speed (so, the magnitude of the final velocity is still u). So the change in momentum is

- For the clay, the final velocity is

since it sticks to the wall. So, the change in momentum is

So we see that the greater momentum change (in magnitude) is experienced by the ball.