Question

A particle starts from the point $(0,8)m$ and moves with uniform velocity of $3\hat{i}$$m/sec$. After $5sec$, the angular velocity of the particle about the origin will be

• A. $\frac{8}{289}rad/\sec$
• B. $\frac{3}{8}rad/\sec$
• C. $\frac{24}{289}rad/\sec$
• D. $\frac{8}{17}rad/\sec$

Answer 1

The correct option is C $\frac{24}{289}rad/\sec$

The unit vector $\hat{i}$ is along the X-axis. Hence the velocity is along the X-axis.
Distance covered in $5sec$ $s=v\times t=3\times 5=15m$
$r=\sqrt{8^2+{15}^2}=\sqrt{289}=17m$


$v\sin \theta$ is the velocity vector about the origin.
Hence, $\omega =\frac{v\sin \theta }{r}=\frac{3}{17}\times \frac{8}{17}=\frac{24}{289}rad/\sec$