two bodies of mass m1 and m2 are attached to two ends of a string which passes over a massless and frictionless pulley. find the acceleration of the bodies and the tension of the string. m1 is bigger than m2

a = [(m1 - m2)/(m1 + m2) ]*g

m1*g -T = m1*a
T = m1*(g-a)
= 2*m1*m2*g/(m1+m2)

To find the acceleration of the bodies and the tension in the string, we can use Newton's second law of motion and apply it to each body separately.

Let's assume that m1 is the larger mass and m2 is the smaller mass.

1. Start by drawing a free body diagram for each mass.
- For m1, there are two forces acting on it: its weight (mg1) downward and the tension (T) in the string upward.
- For m2, there are also two forces acting on it: its weight (mg2) downward and the tension (T) in the string upward.

2. Next, apply Newton's second law of motion to each mass.
- For m1: ΣF = m1 * a, where ΣF is the net force acting on m1.
Since m1 is larger, the net force acting on it is the difference between its weight and the tension: mg1 - T = m1 * a.
- For m2: ΣF = m2 * a. Since m2 is smaller, the net force acting on it is the sum of its weight and the tension: T - mg2 = m2 * a.

3. Since the mass of an object is given by m = ρ * V, where ρ is the density and V is the volume, and assuming the density is constant, we can express the weight of each object as mg = ρ * V * g. Therefore, the expressions for the forces become:
For m1: ρ1 * V1 * g - T = m1 * a
For m2: T - ρ2 * V2 * g = m2 * a

4. We can rearrange the equations and combine them to solve for the acceleration:
ρ1 * V1 * g - T = m1 * a
T - ρ2 * V2 * g = m2 * a

Add the two equations together to eliminate the tension (T):
ρ1 * V1 * g - ρ2 * V2 * g = (m1 + m2) * a

Simplify the equation to solve for the acceleration (a):
a = (ρ1 * V1 * g - ρ2 * V2 * g) / (m1 + m2)

5. Once you've found the acceleration, you can substitute it back into one of the earlier equations to find the tension (T).
For example, using the equation for m1:
ρ1 * V1 * g - T = m1 * a

Rearrange the equation to solve for T:
T = ρ1 * V1 * g - m1 * a

Now you have the acceleration of the bodies (a) and the tension in the string (T).