Question

In the system of two pulleys connected as shown in the figure, M₁ = 4M₂ and mass M₁ is 20 cm above the ground, whereas mass M₂ is lying on the ground. Find the distance covered by when the system is released. (g = 10 m/s²).

Answer 1

To find the constraint relation between accelerations of M1 and M2 , measure their distances from fixed pulley A. Apply Newton’s second law in vertical direction for each block.

M₁ = 4M₂

As M₁ is heavier, it will move down with acceleration a and M₂ will move upward with acceleration 2a because the strings around the pulley B will move through half the distance as compared to that of A.

∴ M₁g - 2T = M₁aT - M₂g = M₂ x 2a or a = g/4.

Therefore, the time taken for M₁ to reach the ground at 20 cm distance

Distance covered by M₂ with velocity 2ms-1upwards before coming to rest

Distance covered by M₂ before coming to rest = x = x₁ + x₂

= 0.4 + 0.2

= 0.6 m