Question

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

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

Answer 1

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



$\omega =\frac{V_{\perp }}{r}$
$\omega =\frac{3\cos \theta }{r}$
$\omega =\frac{3}{r}\times \frac{8}{r}=\frac{24}{r^2}$
In $\Delta OAB$
$r^2=(15{)}^2+(8{)}^2=289$
$\omega =\frac{24}{289}\text{rad/s}$