Question

$5$ balls of mass $1\text{kg},2\text{kg},3\text{kg},4\text{kg}$ and $5\text{kg}$ are tied in a horizontal plane with the massless rod as shown in figure. Balls are rotating about $X{X}^{\prime }$ axis with constant angular velocity $\omega =10\text{rad/s}$. Find the magnitude of angular momentum [in ${\text{kg m}}^2\text{/s}$] about axis $X{X}^{\prime }$.

• A. $750$
• B. $500$
• C. $2000$
• D. $1000$

Answer 1

The correct option is C $2000$

As we know,
${\overrightarrow{L}}_{\text{system}}=I_{\text{axis}}.\omega$
Here, $I_{\text{axis}}=m_1{r}_1^2+m_2{r}_2^2+m_3{r}_3^2+m_4{r}_4^2+m_5{r}_5^2$
$I_{\text{axis}}=1\times 2^2+2\times 4^2+3\times 1^2+4\times 3^2+5\times 5^2$
$I_{\text{axis}}=4+32+3+36+125$
$I_{\text{axis}}=200{\text{kg m}}^2$
Hence,
$L_{\text{system}}=I_{\text{axis}}.\omega$
$=200{\text{kg-m}}^2\times 10\frac{\text{rad}}{\text{s}}$
$=2000{\text{kg-m}}^2\frac{\text{rad}}{\text{s}}$
i.e $\left|\overrightarrow{L}\right|=2000{\text{kg-m}}^2\frac{\text{rad}}{\text{s}}$