51) Two blocks of masses 2 kg and 4 kg are hanging with the help of massless passing over an ideal pulley inside an elevator. The elevator is moving upward with an acceleration $\frac{g}{2}$. The tension in the string connected between the blocks will be $(Take g=10 m/s^2).$
$$\begin{gathered} \left(1\right) 40 N \\ \left(2\right) 60 N \\ \left(3\right) 80 N \\ \left(4\right) 20 N \end{gathered}$$

Inside the lift the frame of reference (attached to the floor or celing) is moving up with an acceleration of g/2 upwards. So for applying Newton's laws, we need to add a pseudo force of mass*g/2 in the downward direction for each mass. In other words, we can say the effective g' = g + g/2 = 3g/2 downwards. Since M1, the 4 kilo mass is heavier, it will accelerate downwards with in the lift. M2, the 2kg mass will move upwards with the same acceleration as that of M1. We assume that the string is tight and so it has the same tension T through the string. equations of motions for M1 and M2 are : M1 g' - T = M1 a => a = ( g' - T/M1) M2 a = T - M2 g' => T = M2 (a+g') = M2 (2g' - T/M1) T = 2 M2 g' - T M2 / M1 => T = 2 M1 M2 g' / (M1+M2) T = 3 M1 M2 g / (M1+M2) = 3 *2 * 4 * 10 / (2+4) = 40 Newtons T = 3 M1 M2 g / (M1+M2) = 3 *2 * 4 * 10 / (2+4) = 40 Newtons