Question

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

Answer 1

this question is based on concept of Psuedo force. Let acceleration of the system be a.
a/c to question ,
m1 and m2 doesn't slide down. means, m1 and m2 are rest with respect to M.

now draw free body daigram for m1 and m2
in case of m1,
T = m1a ........(1)

in case of m2,
T = m2g........(2)

from eqs. (1) and (2),
a = m2g/m1

hence, $a=\frac{m_2}{m_1}g$

Answer 2

hope it is helpful to you..