Question

A system consists of block A and B of same mass $5kg$ and connected to the pulley as shown in figure. Find the minimum relative acceleration with which they will move?
(Take $g=10m/s^2$)

• A. $8m/s^2$
• B. $5m/s^2$
• C. $4m/s^2$
• D. $16m/s^2$

Answer 1

The correct option is D $16m/s^2$

Static friction between two blocks,
$f_{2smax}={\mu }_{2s}\times 5g=30N$
Since $f_{2smax}<F$, the blocks will move and hence, friction will be kinetic.
Drawing FBD of both blocks

Friction between A and B,
$f_{2k}={\mu }_{2k}\left(5g\right)=0.4\left(50\right)=20N$

Both will move with the same acceleration in opposite direction, (because they are connected by a string)

Let us write equations of motion for both blocks A and B.
For Block B:
$T-f_{2k}=m_{B}a$
i.e $T-20=5a------\left(1\right)$
For Block A:
$F-T-f_{2k}=m_{A}a$
$120-T-20=5a-----\left(2\right)$

Adding (1) and (2), $80=10a$
or $a=8m/s^2$
As both the block are moving in upposite direction. So, the relative acceleration is $16m/s^2$