An object of mass 50kg and another 100kg are tied to the end of a light inextensible string.The string passes over a smooth pulley. Determine the tension in the string?

To determine the tension in the string, we need to consider the forces acting on the two objects.

For the 50kg object:
- Weight (W) = mass x acceleration due to gravity = 50kg x 9.8 m/s^2 = 490 N
- Tension in the string (T) is acting upwards

For the 100kg object:
- Weight (W) = mass x acceleration due to gravity = 100kg x 9.8 m/s^2 = 980 N
- Tension in the string (T) is acting upwards

Since the objects are connected by a light inextensible string passing over a smooth pulley, the tension in the string will be the same for both objects. Let's denote this tension as T.

Now, we can set up equations of motion for the two objects:
For the 50kg object:
T - 490 = 50a (where a is the acceleration of the system)

For the 100kg object:
980 - T = 100a

Since the objects are connected by the same string, their accelerations will be the same. Therefore, we can set the two equations equal to each other:
T - 490 = 50a
980 - T = 100a

Solving these two equations simultaneously, we get:
T = 640 N

Therefore, the tension in the string is 640 N.

Let the tension in the string be T.

For the 50kg mass:

$$T - mg = ma$$ $$T - 50 \times 9.8 = 50a$$ $$T = 50a + 490$$

For the 100kg mass:

$$mg - T = ma$$ $$100 \times 9.8 - T = 100a$$ $$T = 100a + 980$$

Equating the two expressions for T:

$$50a + 490 = 100a + 980$$ $$50a = 490$$ $$a = 9.8 m/s^2$$

Substituting a back into the expression for T:

$$T = 50a + 490$$ $$T = 50 \times 9.8 + 490$$ $$T = 980N$$

Therefore, the tension in the string is 980N.