Three blocks $$M_1, M_2, M_3$$ having masses $$4 \text{ kg}, 6 \text{ kg}$$ and $$10 \text{ kg}$$ respectively are hanging from a smooth pulley using rope 1, 2 and 3 as shown in figure. The tension in the rope 1, $$T_1$$ when they are moving upward with acceleration of $$2 \text{ ms}^{-2}$$ is ______ N (if $$g = 10 \text{ m/s}^2$$).

All three masses move upward with acceleration a=$$2 \text{ ms}^{-2}$$

Total mass:

$$m_{total}=4+6+10=20kg$$

Now treat the three blocks as a single body.

Forces on the system:

• Upward: $$T_1$$
• Downward: total weight $$=20g$$

Apply Newton’s second law (upward positive):

$$T_1-20g=20\times2$$

Substitute $$g = 10 \text{ m/s}^2$$

$$T_1-200=40$$

$$T_1=240N$$

Final answer: 240 N