A trolley of mass 20 kg is attached to a block of mass 4 kg by u massless string passing over a frictionless pulley as shown in the figure. If the coefficient of kinetic friction between the trolley and the surface is 0.02, then the acceleration of the trolley and block system is

[ Take $g=10 m s^{-2}$]

 

 

As the string is inextensible, and the pulley is smooth, therefore both the $4 kg$ block and the $20 kg$ trolley have the same acceleration $a$.

Let $T$ be tension in the string. 

The equation of motion of the block is $40-T=4a \dots \left(i\right)$

 The equation of motion of the trolley is $T-f_k=20a$

$$\begin{gathered} f_k={\mu }_{k}N \\ Here, {\mu }_k=0.02, N=20\times 10\Rightarrow N=200 N \\ \therefore T-0.02\times 200=20a or T-4=20a \dots \left(ii\right) \\ Adding \left(i\right) and \left(ii\right), we get, \\ a=\frac{36}{24} m s^{-2} \\ =1.5 m s^{-2} \end{gathered}$$