Question

In the system shown in figure, pulley is massive and rope does not slip over it. Then acceleration of the block is __________(Treat pulley as a child cylinder)

• A. $\frac{F}{m}$
• B. $\frac{2(F-mg)}{3m}$
• C. $\frac{2mg}{3}$
• D. $\frac{2(F+mg)}{3m}$

Answer 1

Answer: (A)

$\frac{F}{m}$

$\begin{array}{c}\text{Correct option is (A)}\\ \text{If there is no slipping}a=\alpha R\\ \begin{array}{c}T=I\alpha \\ FR=m{R}^2\alpha (I_{\text{(cylinder}}=m{R}^2)\\ \frac{F}{m}=\alpha R\end{array}\\ \frac{F}{m}=a\end{array}$