A block of mass 4.44 kg lies on a frictionless horizontal surface. The block is connected by a cord passing over a pulley to another block of mass 6.55kg which hangs in the air , as shown above. Assume the cord to be light (massless and weightless) and unstretchable and the pulley to have no friction and no rotational inertia.

To solve this problem, we need to analyze the forces acting on each block and use Newton's laws of motion.

Let's start by understanding the forces on the hanging block, which has a mass of 6.55 kg. Since it is hanging freely, the only force acting on it is its weight (mg), where g is the acceleration due to gravity (approximately 9.8 m/s^2).

Next, let's consider the block on the horizontal surface, which has a mass of 4.44 kg. Since the surface is frictionless, the only force acting on it is its weight (mg). However, since the cord is connected to this block and passes over a pulley, there will also be a tension force (T) acting on the block.

Now, we need to consider the motion of the system. Since the cord is light, unstretchable, and the pulley is frictionless, the tension in the cord is the same on both sides.

Using Newton's second law (F = ma), we can write down the equations for each block:

For the hanging block:
mg - T = ma1, where a1 is the acceleration of the hanging block.

For the block on the horizontal surface:
T - mg = ma2, where a2 is the acceleration of the block on the surface.

Since the two blocks are connected by the cord and share the same acceleration (a1 = a2 = a), we can simplify the equations:

mg - T = ma
T - mg = ma

Now, let's solve for the acceleration:

Adding both equations, we have:

2mg = 2ma
simplifying, we get:
g = a

So, the acceleration of the system is equal to the acceleration due to gravity.

To find the tension force (T), we can substitute the value of acceleration (a = g) into one of the equations:

T - mg = ma
T - mg = mg

Simplifying, we find:

T = 2mg

Substituting the value of mass (m = 4.44 kg) and acceleration due to gravity (g = 9.8 m/s^2), we get:

T = 2 * 4.44 kg * 9.8 m/s^2

Calculating this expression, we find:

T ≈ 86.74 N

Therefore, the tension in the cord is approximately 86.74 Newtons.