Question

A solid cylinder $A$ of mass $12kg$ is being pulled by another weight $B$ ( $3kg$ ) along the horizontal plane as shown in figure (pulley is massless). The weight $B$ is attached to the end of a string wound around the circumference of cylinder. If there is no slipping anywhere and string is inextensible, then find acceleration (in $m{s}^{-2}$ ) of $A$

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (B)

For Translation of $A$ :
$T+f=ma...(i)$
For Rotational motion of $A$ :
$\left(T-f\right)R=I\alpha =\left(\frac{m{R}^2}{2}\right)\alpha ...(ii)$
Condition for pure rolling : $a=\alpha R...(iii)$
Using equation $(i),(ii),(iii)$ :
$T=\frac{3}{4}ma=9a...(iv)$
For Translation of $B$ :
$3g-T=3a$
Using equation $(iv)$ :
$a=\frac{g}{5}m/s^2$