A system to 10 balls each of mass $$2$$ kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the $$7^{th}$$ and $$8^{th}$$ ball is ______ N when $$6^{th}$$ ball just leaves the table.

Step 1: Acceleration of system
When the 6th ball just leaves the table:

• Number of hanging balls = 6
• Driving force = 6mg N
• Total mass of system = 10m

$$a=\frac{\text{net force}}{\text{total mass}}=\ \frac{\ 6mg}{10m}=\ \frac{\ 3g}{5}$$

​Step 2: Tension between 7th and 8th ball

Consider the last 3 balls (8th, 9th, 10th) lying on the table:

• Mass of these 3 balls = 3m
• They move with same acceleration $$a=\frac{3g}{5}$$

$$T=(\text{mass})\times(\text{acceleration})$$

 $$T=3m\cdot\frac{3g}{5}$$

$$substitute\ m=2kg,g=10m/s^2:$$

$$T=3\times2\times\ \frac{\ 3\times\ 10}{5}​=36N$$

Final Answer:

36 N