Question

A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should be unbinding the strings to achieve a speed of $4\text{m/s}$, is $cm$. (Take $g=10m/s^2$).

• A. 120
• B. 120.00
• C. 2
• D. 120.0

Answer 1

Answer: (A), (B), (C), (D)

Angular acceleration due to the torque produced by the tension force in the string is given as:
$\alpha =\frac{\left(mg\right)\left(r\right)}{\frac{3}{2}m{r}^2}=\frac{2g}{3r}$

Thus the linear acceleration is:
$\Rightarrow a=\frac{2g}{3}$
Now applying equation of motion we can write:
$v^2=u^2+2as$
Initially cylinder is at rest:
$\Rightarrow v^2=2as$

$16=\frac{40}{3}\times s\Rightarrow s=0.3\times 4=120\text{cm}$