Question

A puck of mass $m=1.50\text{kg}$ rotates in a circle of radius $r=20\text{cm}$ on a frictionless table while attached to a hanging cylinder of mass $M=2.50\text{kg}$ by means of a cord that extends through a hole in the table as shown in the figure. What speed of the puck is required to keep the cylinder at rest?

• A. $0.85\text{m/s}$
• B. $1.81\text{m/s}$
• C. $2.52\text{m/s}$
• D. $3.62\text{m/s}$

Answer 1

The correct option is B $1.81\text{m/s}$

Given that
$m=1.50\text{kg}$
$M=2.50\text{kg}$
$r=20\text{cm}=0.20\text{m}$

FBD of the given system is,


So, $T=Mg----\left(1\right)$
and, $T=\frac{m{v}^2}{r}----\left(2\right)$

From equation $\left(1\right)$ and $\left(2\right)$,
$\frac{m{v}^2}{r}=Mg$
$\Rightarrow v=\sqrt{\frac{Mgr}{m}}$
$\Rightarrow v=\sqrt{\frac{\left(2.50\right)\left(9.80\right)\left(0.20\right)}{1.50}}$
$\Rightarrow v=1.81\text{m/s}$
Hence, option $\left(b\right)$ is correct.