Let's go through each part of the question from the image step by step:

Part 1: Tension $T_2$

• In this system, we have three blocks with masses of 10 kg, 7 kg, and 4 kg. These masses are connected by pulleys, and the system is in equilibrium.
• The equilibrium condition means that the forces acting on the blocks should balance out.

For the masses hanging off the pulleys, the forces due to gravity are:

• Force on the 4 kg block: $F_1 = 4 \times 9.8 = 39.2 \, \text{N}$
• Force on the 7 kg block: $F_2 = 7 \times 9.8 = 68.6 \, \text{N}$

Since the system is in equilibrium, the tensions $T_1$ and $T_2$ must balance these forces. Therefore:

• $T_1 = 39.2 \, \text{N}$
• $T_2 = 68.6 \, \text{N}$

Part 2: Frictional Force

In this part, there is a mention of a frictional force between the 10 kg block and the table.

• The frictional force can be calculated using $f = \mu N$, where $\mu$ is the coefficient of friction and $N$ is the normal force.
• The normal force here is equal to the weight of the 10 kg block, which is $N = 10 \times 9.8 = 98 \, \text{N}$.

Without the coefficient of friction $\mu$, we cannot find the exact friction force, but this setup suggests that there is a frictional force preventing motion as the system is in equilibrium.

Part 3: Resultant Force on 10 kg Block

If the maximum frictional force is not sufficient to keep the system in equilibrium, the resultant force on the 10 kg block would be:

• The correct answer from the options would be $T_2 - T_1 - F$, because if friction is insufficient, the 10 kg block would accelerate in the direction of the net force, which is the difference between the tensions $T_2$ and $T_1$, minus the opposing frictional force.

Part 4: Tension and Angles in Strings (AP and BP)

This question describes a particle suspended by two strings.

• The weight of the particle is 20 N.
• The tensions in the strings are given as $a8$ and $6b$, which likely means some constants $a$ and $b$ need to be calculated.

To solve for the tensions and angles, more specific numerical values are required, especially for constants like $a$ and $b$.

Would you like me to provide further details or solve one of these parts step by step?

Follow-up Questions:

1. How would the system behave if the friction coefficient was known? Can we calculate the exact frictional force?
2. What would happen if one of the blocks' mass was increased? How would it affect the tensions?
3. How do we account for pulley friction or rotational inertia in more complex scenarios?
4. Could we analyze a similar system with inclined planes instead of horizontal tables?
5. What if the coefficient of friction between the block and table were dynamic (changing as the block moves)?

Tip:

Always begin by analyzing forces acting on each mass in such systems, and consider the direction of tensions to avoid sign errors.