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Two masses m and 2m are attached with each other by a rope passing over a frictionless and massless pulley. If the pulley is accelerated upwards with an acceleration ‘a’, what is the value of T?

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    If the pulley is accelerated at rate a, it is the same as if the weights became m(g +a) and 2m(g+a), in a coordinate system moving with the pulley, with gravitational accleration g + a.

    There would be additional acceleration of the weights at a rate
    a' = (g+a)(m/3m) = (g+a)/3
    (2m would accelerate at rate a' down and m would accelerate up)

    For the cable tension, let us apply Newton's second law to 2m.

    2m*(g+a)-T = 2m*a' = 2m*(g+a)/3

    T = 2m*(g+a)(2/3)= (4m/3)(g+a)

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