Question

A particle undergoes uniform circular motion. The velocity and angular velocity of the particle at an instant of time are $\overrightarrow{v}=3\hat{i}+4\hat{j}\text{m/s}$ and $\overrightarrow{\omega }=x\hat{i}+6\hat{j}\text{rad/s}$. The value of $x$ in $\text{rad/s}$ is

• A. $8$
• B. $6$
• C. $-8$
• D. $-6$

Answer 1

The correct option is C $-8$

For a particle under uniform circular motion, $\overrightarrow{v}.\overrightarrow{\omega }=0\Rightarrow \overrightarrow{v}\perp \overrightarrow{\omega }$
$\therefore \overrightarrow{v}.\overrightarrow{\omega }=(3\hat{i}+4\hat{j}).(x\hat{i}+6\hat{j})=0$
$\Rightarrow 3x+24=0$
$\Rightarrow x=-8\text{rad/s}$