[tex]\sf{m_1}[/tex] = 8kg
[tex]\sf{m_2}[/tex] = 4kg
g = 10m/s²
→Acceleration of block
→Tension in strings
Let, the two equation will be ,
[tex]\leadsto[/tex] 8g - T = 8a ..... Equation no (1)
[tex]\leadsto[/tex] T - 4g = 4a ..... Equation no (2)
Putting the value of equation no (1) and (2) we get,
[tex]\implies[/tex] 4g = 12a
[tex]\implies[/tex] 4 × 10 = 12a
[tex]\implies[/tex] 40 = 12a
[tex]\implies[/tex] a = [tex]\sf\dfrac{\cancel{40}}{\cancel{12}}[/tex]
[tex]\dashrightarrow[/tex] a = [tex]\dfrac{10}{3}[/tex]
Again, we have to putting the value of a in the equation no (2) we get,
[tex]\implies[/tex] T - 4g = 4 × [tex]\dfrac{10}{3}[/tex]
[tex]\implies[/tex] T - 4 × 10 = 4 × [tex]\dfrac{10}{3}[/tex]
[tex]\implies[/tex] T - 40 = [tex]\dfrac{40}{3}[/tex]
[tex]\implies[/tex] T = [tex]\dfrac{40}{3}[/tex] + 40
[tex]\implies[/tex] T = [tex]\dfrac{40 + 120}{3}[/tex]
[tex]\dashrightarrow[/tex] T = [tex]\dfrac{160}{3}[/tex] N
[tex]\therefore[/tex] Acceleration of block = [tex]\dfrac{10}{3}[/tex] m/s².
And, Tension in strings = [tex]\dfrac{160}{3}[/tex] N
