In the figure shown ,the string and pulley are massless , if m1 = 15 kg and m 2 =10 kg ,the tension in the string is ;

To find the tension in the string, we can use Newton's second law of motion which states that the sum of the forces acting on an object is equal to its mass multiplied by its acceleration. In this case, we can consider the system of masses m1 and m2 as one object.

Step 1: Identify the forces acting on the system.
In this system, there are two forces acting on the masses: the weight force (mg) and the tension force in the string (T).

Step 2: Write down the equations for the forces acting on the masses.
For m1: T - m1g = m1a (eqn 1)
For m2: m2g - T = m2a (eqn 2)

Step 3: Solve the equations simultaneously.
Since the masses are connected by the same string and move together, they will have the same acceleration (a). We can equate the accelerations in equations 1 and 2:

m1a = m2a

Since the mass of the system is the sum of the individual masses:

(m1 + m2)a = m1a + m2a

Simplifying this equation, we get:

(m1 + m2)a = T - m1g + m2g

Step 4: Calculate the tension in the string.
Rearrange the equation to solve for T:

T = (m1 + m2)g

Substituting the given values:

T = (15 kg + 10 kg) × 9.8 m/s^2
T = 25 kg × 9.8 m/s^2
T = 245 N

Therefore, the tension in the string is 245 Newtons.