Question

A trolley of mass $20kg$ is attached to a block of mass $4kg$ by a massless string passing over a frictionless pulley as shown in the figure. If the coefficient of kinetic friction between trolley and the surface is $0.02$, then the acceleration of the trolley and block system is
(Take$g=10m{s}^{-2}$)

• A. $1m$ $s^{-2}$
• B. $2m$ $s^{-2}$
• C. $1.5m$ $s^{-2}$
• D. $2.5m$ $s^{-2}$

Answer 1

Answer: (C)

As the string is inextensible, and the pulley is smooth, therefore both the $4kg$ block and the $20kg$ 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
$T$ $-f_k$ $=20a$
$f_k$ $={\mu }_k$ $N$
Here, ${\mu }_k$ $=0.02,N$ $=20\times 10$ $=200N$
$\therefore$ $T-0.02\times 200$ $=20a$ or $T-4=20a$ $\dots \left(ii\right)$
Adding (i) and (ii), we get, $a=\frac{36}{24}m{s}^{-2}$ $=1.5m{s}^{-2}$