Two blocks of equal mass m are tied to each other through a light string . One of the blocks is pulled along the line joining them with a constant force F . Find the tension in the string joining the blocks.

To find the tension in the string joining the blocks, we can analyze the forces on each block separately.

Let's denote the tension in the string as T.

For the block being pulled with force F:
- There is a force of tension T acting in the opposite direction.
- There is a force of friction opposing the motion, which we'll denote as Friction1.

For the other block:
- There is a force of tension T acting in the same direction.
- There is an equal force of friction opposing the motion, which we'll denote as Friction2.

Since the blocks are tied together, they have the same acceleration. Therefore, we can assume that the frictional forces on both blocks are equal in magnitude.

Now, let's apply Newton's second law (F = ma) to each block.

For the block being pulled:
F - Friction1 = ma1, where a1 is the common acceleration.

For the other block:
T - Friction2 = ma2, where a2 is the same common acceleration.

Since the blocks have the same mass, m, we can rewrite these equations as:
F - Friction1 = m * a, and T - Friction2 = m * a, where a is the common acceleration.

Since the acceleration is the same for both blocks, we can eliminate them from the equations.

Combining the equations for friction:
Friction1 = Friction2

Substituting this into the equation for tension:
F - Friction1 = T - Friction2

Simplifying:
F = T

Therefore, the tension in the string joining the blocks is equal to the force applied to the block being pulled, F.

F=totalmass*a

F=(2M)a
a= F/2M

but this is the a for each block, so the tension pulling the second block is

tension= ma= m(F/2m)=1/2 F