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The tension in the cable supporting a lift moving upwards is twice the tension when the lift moves downwards. What is the acceleration of the lift?

The tension in the cable supporting a lift moving upwards is twice the tension when the lift moves downwards. What is the acceleration of the lift? Correct Answer g/3

Concept:

Let lift is moving in an upward direction with acceleration ‘a’.

Tension in the string (T1)  = m(g+a) where m is the mass of lift.

Let lift is moving in a downward direction with acceleration ‘a’.

Tension in the string (T2) = m(g-a)

T1 = 2T2  (given)

m(g+a) = 2m (g-a)

a = g/3

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