Question
GeneralGeneralGeneral

As shown in the figure, two blocks of 4 kg and one block of 6 kg are connected through a pulley system. Find the ratio T₁/T₂.

Verified Answer

The arrangement consists of an Atwood machine where the left side has a 4 kg block and the right side effectively carries a 4 kg block connected to a 6 kg block.

Total mass on the right side:

4 + 6 = 10 kg

Let acceleration of the system be a.

For the left 4 kg block moving upward:

T₁ − 4g = 4a

Therefore:

T₁ = 4g + 4a

For the combined right side:

10g − T₁ = 10a

Substituting T₁:

10g − (4g + 4a) = 10a

6g = 14a

a = 3g/7

Now:

T₁ = 4g + 4(3g/7)

T₁ = 40g/7

For the 6 kg block:

6g − T₂ = 6a

Substituting a = 3g/7:

6g − T₂ = 18g/7

T₂ = 24g/7

Therefore:

T₁/T₂ = (40g/7)/(24g/7)

T₁/T₂ = 40/24

T₁/T₂ = 5/3

Hence, the required ratio is:

T₁/T₂ = 5/3