Question

In the arrangement shown in the figure neglect the masses of the pulley and string and also friction. The accelerations of blocks A and B are

• A. g, g/2
• B. g/2,g
• C. 3g/2, 3g/4
• D. g,g

Answer 1

The correct option is D g,g

Free body diagrams for two mass blocks and two pulleys are given in figure.

Force balance equations for all the cases are given below

For $m_1$:

$T-m_1\times g=m_1\times a_1$ ..........(1)

For $m_2$:

$m_2\times g-T_2=m_2\times a_2$ .........(2)

For pulley $P_1$:

$2\times T-T=0\times a_1{P}_1$ ..........(3)

For pulley $P_2$:

$T_2-2\times T=0\times a_2{P}_2$ ............(4)

By solving equation (1),(2),(3) and (4), we get

$a_1=g$ and $a_2=g$

Hence both blocks are moving downwards with acceleration $gm/s^2$