Question

In the drawing, the rope and the pulleys are massless, and there is no friction. The larger block has a mass of 10.03kg and the smaller block has a mass of 3.85kg.

Answer 1

As you haven't exactly given about what to find. I am assuming that we have to find the acceleration of both the blocks and the tension in the rope.

Let, the acceleration of smaller block be a

Then the acceleration fo bigger block will be 2a, because, as the smaller slides down say x distance, the bigger block will slide 2x distance on the surface (As 2x length of the rope is used near the smaller block)

Let the tension in the wire be T

Now, writing the force equation on smaller block

Ms * g - 2 * T = Ms * a .............I

Now, writing the force equation on bigger block

T = Mb * 2 * a ..............II

Substituting II in I

Ms * g - 2 * Mb * 2 * a = Ms * a

Ms * g = 4 * Mb * a + Ms * a

substituting the values

3.85 * 9.81 = 4 * 10.03 * a + 3.85 * a

37.7685 = 43.97 * a

=> a = 0.859 m/s^2

Substituting the value of a in II

T = 10.03 * 2 * 0.859

T = 17.231 N

Acceleration of the smaller block = 0.859 m/s^2

Acceleration of the bigger block = 1.718 m/s^2

Tension in the string = 17.231 N