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 $ms^{- 2}$ ) of $A$

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (B)

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