Determine the acceleration of the 5kg block A. Neglect the mass of the pulley and cords. The block B has a mass of 10kg. The coefficient of kinetic friction between block B and the surface is ${\mu }_k=0.1$. (Take, $g=10 \mathrm{m}/{\mathrm{s}}^2$ )

Suppose T be the tension in the string attached to block B. Then tension in the string connected to block A would be 4 T.

Similarly, if a be the acceleration of block A (downwards), then acceleration of block B towards right will be 4 a.

Equations of motion are

For block $A, m_{A}g-4T=m_{A}a$ or

 50-4 T=5 a                        …………………(i)

 T-f=10(4 a)

or

$T-(0.1)\left(10\right)\left(10\right)=40a$

or

$T-10=40a$                      ……………….(ii)

Solving Equatons (i) and (ii), we get

$a=\frac{2}{33} \mathrm{m}/{\mathrm{s}}^2$