A light string passes over a frictionless pulley. To one of its ends a mass of 6kg is attached to the other end mass of 10kg is attached. The tension of the thread isa) 24.5Nb) 2.45Nc) 79Nd) 73.5N

To find the tension in the string, we need to consider the forces acting on both masses. Since the pulley is frictionless, we assume that there is no energy loss due to friction.

Let's consider the two masses separately:

Mass of 6 kg:
The force acting on this mass is its weight, which is given by:
Force_6kg = Mass_6kg * gravitational acceleration
Force_6kg = 6 kg * 9.8 m/s^2 ≈ 58.8 N

Mass of 10 kg:
The force acting on this mass is also its weight:
Force_10kg = Mass_10kg * gravitational acceleration
Force_10kg = 10 kg * 9.8 m/s^2 ≈ 98 N

Now, let's consider the tension in the string. The tension in the string is the same on both sides of the pulley due to its massless and frictionless nature. Therefore, we can equate the two tensions:

Tension = Tension_6kg = Tension_10kg

Since the masses are connected by the string passing over the pulley, the tension force on the 6 kg mass side pulls upward, while the tension force on the 10 kg mass side pulls downward.

Now, to find the tension, we can set up equations for both masses:

For the 6 kg mass (upward direction):
Tension - Force_6kg = Mass_6kg * acceleration (since it is accelerating upward)
Tension - 58.8 N = 6 kg * a1 (where a1 is the acceleration)

For the 10 kg mass (downward direction):
Force_10kg - Tension = Mass_10kg * acceleration (since it is accelerating downward)
98 N - Tension = 10 kg * a2 (where a2 is the acceleration)

Since the masses are connected by the string and the string does not stretch, their accelerations are the same (magnitude but opposite in direction):

a1 = -a2

Now we can solve for the tension:

Tension - 58.8 N = 6 kg * (-a2)
Tension + 58.8 N = 6 kg * a2

98 N - Tension = 10 kg * a2

Now, we can solve for Tension:

Adding the two equations together:

Tension + 58.8 N + (98 N - Tension) = 6 kg * a2 + 10 kg * a2
156.8 N = 16 kg * a2

a2 = 156.8 N / 16 kg
a2 ≈ 9.8 m/s²

Now, we can find the tension by substituting the value of a2 into one of the equations:

Tension + 58.8 N = 6 kg * 9.8 m/s²
Tension + 58.8 N = 58.8 N

Now, isolate the Tension:

Tension = 58.8 N - 58.8 N
Tension = 0 N

So, the tension in the string is 0 N. None of the provided options (a) 24.5 N, b) 2.45 N, c) 79 N, d) 73.5 N) is correct.

The result may seem counterintuitive, but it occurs because the two masses have the same weight, and they are perfectly balanced due to the pulley's configuration. Therefore, the tension in the string is zero.