Two masses of 5 kg and 3 kg are suspended with the help of massless inextensible strings as shown in the figure. The whole system is going upwards with an acceleration of 2 m s^-2. The tensions T₁ and T₂ are respectively (Take g = 10 m s^-2)

 

The free body diagram of 3 kg block is as shown in the figure (a)

The equation of motion of 3 kg block is 

$$\begin{gathered} T_2-3g=3a \\ T_2=3(a+g) \\ =3(2+10) \\ =36 N \dots \left(i\right) \end{gathered}$$

The free body diagram of 5 kg is as shown in figure (b)

The equation of motion for 5 kg block is 

$$\begin{gathered} T_1-T_2-5g=5a \\ T_1=5(a+g)+T_2 \\ =5(2+10)+36 (U\sin g (i\left)\right) \\ =96 N \end{gathered}$$