Given: 5a + T − 5g = 0

From free-body diagram (1), T = 5g − 5a …..(i)

⇒ T − 8g − 16a = 0

From free-body diagram (2),

T = 8g + 16a ……(ii)

From equations (i) and (ii), we get:

5g − 5a = 8g + 16a

So, the acceleration of the 5 kg mass is 97 m/s2 upward and that of the 4 kg mass is 2a= downward.

(b) From free body diagram (3),

⇒ 8a − T = 0

⇒ T = 8a

Again, T + 5a − 5g = 0

From free body diagram-4, 8a + 5a − 5g = 0

⇒ 13a − 5g = 0

downward

(c) T + 1a − 1g = 0

From free body diagram, T = 1g − 1a …..(i)

Again, from free body diagram

⇒ T − 4g − 8a = 0 …..(ii)

From equation (i) 1g − 1a − 4g − 8a = 0

downward

∴ Acceleration of mass 1 kg is upward, Acceleration of mass 2 kg is downward