Question

the acceleration of block M1 and M2 with respect to pulley in the condition shown in figure will be

Answer 1

Here is the diagram of a pulley system which comprises two masses  $m_{1} \ and\ m_{2} \ respectively$

     $Here\ m_{1}=2kg$

                 $m_{2}=4kg$

The masses are connected to the two ends of a rope passing over the pulley.

As per the question, the pulley is friction less.

We are asked to calculate the acceleration of two blocks.

As the rope is same on both the sides of the pulley, and the pulley is friction less as well as mass less, so, the acceleration of each block will be same in magnitude but opposite in direction.The mass 2 kg will move vertical upward while the mass 4 kg will move downward with respect to pulley.

The acceleration of each block of such a pulley system is calculated as -

                                   $a\ =\frac{m_{2}- m_{1}} {m_{2}+ m_{1}} \ *g$    

Here g is the acceleration due to gravity.

The value of   $g=9.8\ m/s^2$

                                           $=\frac{4-2}{4+2}\ *10\ m/s^2$

                                           $=\frac{2}{6}\ *10\ m/s^2$

                                           $=\frac{10}{3}\ g\ m/s^2$

Hence the correct answer to the question is option C.