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.

see other post.

F/2

To find the tension in the string joining the blocks, we need to consider the forces acting on each block.

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

For the block being pulled:
1. Force F is acting on it in the direction of the pull.
2. Tension T is acting on it in the opposite direction.

For the other block:
1. Tension T is acting on it in the direction towards the pulled block.
2. The gravitational force mg is acting downward.

Since the blocks are of equal mass, we assume that the gravitational force acting on each block is the same (mg).

Now, let's analyze the forces acting on each block:

For the block being pulled:
- Net force = F - T (Force F in the forward direction, tension T in the opposite direction)

By Newton's second law (F = ma), the net force is equal to the mass times acceleration:
F - T = m*a1 ---- (Equation 1)

For the other block:
- Net force = T - mg (Tension T in the forward direction, gravitational force mg in the opposite direction)

By Newton's second law (F = ma), the net force is equal to the mass times acceleration:
T - mg = m*a2 ---- (Equation 2)

Since the blocks are tied together and connected to the same string, their accelerations must be the same (a1 = a2 = a).

Now, substitute a1 = a2 = a in equations 1 and 2:
F - T = m*a ---- (Equation 1)
T - mg = m*a ---- (Equation 2)

Now, we can solve the system of equations to find the tension T:

Adding equations 1 and 2:
(F - T) + (T - mg) = m*a + m*a
F - mg = 2ma

Rearranging the equation:
T = (2ma - F) + mg

Therefore, the tension in the string joining the blocks is T = 2ma - F + mg.