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11) The two ends A and B of a uniform rod of length L = 1 and mass m are moving with velocities v_{A} and v_{B} _{ }as shown. The angular velocity of the rod is.

$a)20rad/s\phantom{\rule{0ex}{0ex}}b)25rad/s\phantom{\rule{0ex}{0ex}}c)30rad/s\phantom{\rule{0ex}{0ex}}d)50rad/s$

$LetthelinejoiningAtoBbeXaxisandYaxisisperpendiculartotheXaxis.VelocityofpointAwithrespecttoBalongthelinejoiningAandBiszero.\phantom{\rule{0ex}{0ex}}VelocityofAalongXaxistowardsBis{V}_{AX}=20\mathrm{cos}53\xb0=20\times \frac{3}{5}=12m/s\phantom{\rule{0ex}{0ex}}VelocityofBalongXaxistowardsAis{V}_{BX}=V\mathrm{cos}37\xb0=V\times \frac{4}{5}m/s\phantom{\rule{0ex}{0ex}}12=V\times \frac{4}{5}\phantom{\rule{0ex}{0ex}}V=\frac{5\times 12}{4}=15m/s\phantom{\rule{0ex}{0ex}}Angularvelocityofrodis\omega =\frac{VelocityofpointAwithrespecttoBinthedirectionperpendiculartothelinejoiningAandB}{SeparationbetweenAandB}\phantom{\rule{0ex}{0ex}}VelocityofAperpendiculartothelinejoiningAandBis{V}_{AY}=20\mathrm{sin}53\xb0=20\times \frac{4}{5}=16m/s\phantom{\rule{0ex}{0ex}}VelocityofBperpendiculartothelinejoiningAandBis{V}_{BY}=15\mathrm{sin}37\xb0=15\times \frac{3}{5}=9m/s\phantom{\rule{0ex}{0ex}}\omega =\frac{16+9}{1}=25rad/s\phantom{\rule{0ex}{0ex}}Regards\phantom{\rule{0ex}{0ex}}$

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