Miriam Blevins

2023-03-02

A particle undergoes uniform circular motion. The velocity and angular velocity of the particle at an instant of time are $\stackrel{\to }{v}={3}^{i}+{4}^{j}$ m/s and $\stackrel{\to }{\omega }={x}^{i}+{6}^{j}$ rad/s. The value of x in rad/s is A) 8 B)6 C)-8 D)-6

Paola Hays

The correct option is C −8
For a particle moving uniformly in circles, $\stackrel{\to }{v}\stackrel{\to }{\omega }=0⇒\stackrel{\to }{v}\mathrm{\perp }\stackrel{\to }{\omega }\phantom{\rule{0ex}{0ex}}\therefore \stackrel{\to }{v}\stackrel{\to }{\omega }=\left(3\overline{i}+4\overline{j}\right).\left(x\overline{i}+6\overline{j}\right)=0\phantom{\rule{0ex}{0ex}}⇒3x+24=0\phantom{\rule{0ex}{0ex}}⇒x=-8rad/s$

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