Free body diagram:

Assume the system accelerates to the left in the direction of 25 N force (left and up is positive).

Now the tensions in the string will be different because the pulley has a mass of 150 g.

The constraint on the acceleration is a₁ = a₂ = a

Applying Newton's second law for the slab,

25 N - T1 = m₁•a₁

T₁ = 25 N - m₁•a₁ = 25 N - m₁•a ---------------------------------------------(i)

Applying Newton's second law to the pulley,

T₁•R - T₂•R = I•α -------------(as the pulley accelerates anti-clockwise)

(T₁ - T₂) = (I•α)/R

But acceleration a = R•α so α = a/R

(T₁ - T₂) = (I•a)/R²

(T₁ - T₂) = (I•a)/R²

from equation (i),

25 N - m₁•a - T₂= (I•a)/R²

T₂ = 25 N - m₁•a - (I•a)/R² -------------------------------------------------------(ii)

Applying Newton's second law for the mass m2 = 5.0 kg

T₂ - m₂•g = m₂•a₂

T₂ - m₂•g = m₂•a

T₂ = m₂•g + m₂•a --------------------------------------------------------------------(iii)

equating the equations (ii) and (iii),

25 N - m₁•a - (I•a)/R² = m₂•g + m₂•a -------------------------------------------(iv)

here, I = (1/2)(pulley mass)(Radius of pulley)² = (1/2)(0.150 kg)(0.1 m)² = 0.75 × 10^-3 kg-m²

25 N - (4.0 kg)a - ((0.75 × 10-³kg-m²)•a)/(0.1 m)² = (5.0 kg)(9.8 m/s²) + (5.0 kg)a

25 N - (4.0 kg)a - (0.075)a = 49 N + (5.0 kg)a

-(4.0 kg)a - (5.0 kg)a - (0.075)a = 49 N - 25 N

a = -2.64 m/s² [negative sign means the system moves right/down]

T₁ = 25 N - (4.0 kg)(-2.64 m/s²) = -36 N

T₂ = m₂•g + m₂•a = (5.0 kg)(9.8 m/s²) + (5.0 kg)(-2.64 m/s²) = -36 N

The correct answer is option A.