Question

Three small balls of masses $1kg,2kg$ and $3kg$ are moving in a plane and their velocities are $1m/s,2m/s$ and $3m/s$, respectively as shown. The total angular momentum of the system of three balls about point $P$ at given instant of time is:

• A. $8kg{m}^2/s$
• B. $9kg{m}^2/s$
• C. $36kg{m}^2/s$
• D. $7kg{m}^2/s$

Answer 1

Answer: (D)

$7kg{m}^2/s$

The particle of mass $2kg$ is situated perpendicular to the axis of rotation. So, the angle will be ${90}^{\circ }$. Similarly, the particle of mass $1kg$ is situated opposite side of the circular path. So, the angle will be ${90}^{\circ }$ and angular momentum will acts in opposite direction.
According to the diagram, total angular momentum
$=2\times 2\times 2\sin {90}^{\circ }+3\times 3\times 3\sin 0^{\circ }-1\times 1\times 1\sin {90}^{\circ }$
$=8-1$
$=7kg{m}^2/s[\because \sin 0^{\circ }=0$ and $\sin {90}^{\circ }=1]$.