Question

A trolley of mass $20\, kg$ is attached to a block of mass $4\, kg$ 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$\,g=10\,m \,s^{-2}$)

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

Answer 1

Answer: (C)

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
$40 - T = 4a$ $\quad\quad\ldots\left(i\right)$
The equation of motion of the trolley is
$T$ $-f_{k}$ $=20 \,a$
$f_{k}$ $=\mu_{k}$ $N$
Here, $\mu_{k}$ $=0.02, N$ $=20\times10$ $=200\, N$
$\therefore \quad$ $T-0.02\times200$ $=20 a $ or $T-4=20 a$ $\quad\ldots\left(ii\right)$
Adding (i) and (ii), we get, $a=\frac{36}{24} m \,s^{-2}$ $=1.5 m\, s^{-2}$