Three blocks M₁, M₂, M₃ having masses 4 kg, 6 kg and 10 kg respectively are hanging from a smooth pully using rope 1, 2 and 3 as shown in figure. The tension in the rope 1, T₁ when they are moving upward with acceleration of 2ms^–2 is ............... N (if g = 10 m/s²)

The correct answer is 240.

Given data:
Mass of the first block, $M_1=4kg$
Mass of the second block, $M_2=6kg$
Mass of the third block, $M_3=10kg$
Acceleration of the blocks moving upward, $a=2{ms}^{-2}$
Acceleration due to gravity, $g=10{ms}^{-2}$

Step-by-step Derivation:

1. From the given diagram, the three blocks are suspended in series. Rope 1 is connected directly to the pulley and supports all three blocks $M_1$, $M_2$, and $M_3$ hanging below it.

2. Therefore, the total mass supported by Rope 1 ($M_{\mathrm{total}}$) is the sum of the individual masses:
$M_{\mathrm{total}}=M_1+M_2+M_3$
$M_{\mathrm{total}}=4kg+6kg+10kg=20kg$

3. Writing the equation of motion for this combined system of total mass $M_{\mathrm{total}}$ moving upward with an acceleration $a$:
$T_1-M_{\mathrm{total}}g=M_{\mathrm{total}}a$

4. Rearranging the formula to solve for the tension $T_1$:
$T_1=M_{\mathrm{total}}(g+a)$

5. Substitute the values into the equation:
$T_1=20kg\times (10{ms}^{-2}+2{ms}^{-2})$
$T_1=20\times 12$
$T_1=240N$

Thus, the tension in the rope 1 is 240 N.