Question
In the given arrangement all surfaces are smooth. What acceleration should be given to the system, for which the block $m_2$ doesn't slide down?

Answer

(a)

as $m _2$ does not move

therefore $T=m_2 g$

force acting on $m _1$ ==> $ T = m _1 a$

$m _2 g = m _1 a$

$a =\frac{ m _2 g }{ m _1}$

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