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Physics

Mechanics

Easy

Question

A thin uniform rod of mass m and length L is force to rotate about its upper and when it is at rest, it receives an impulse J at its lowest point, normal to its length. immediately, after impact

$Angular velocity of rod is \frac{3 J}{m L}$
$Angular velocity of rod is \frac{2 J}{m L}$
$Angular velocity of rod is \frac{3 J}{2 m L}$
$Angular velocity of rod is \frac{2 J}{3 m L}$

The correct answer is: $text Angular velocity of rod is end text fraction numerator 3 J over denominator m L end fraction$

$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em rowspacing 3 pt end attributes row cell J L equals fraction numerator m L squared over denominator 3 end fraction omega not stretchy rightwards double arrow omega equals fraction numerator 3 J over denominator m L end fraction end cell row cell text Kinetic energy of the rod is end text 1 half fraction numerator m L squared over denominator 3 end fraction omega squared equals 1 half fraction numerator m L cubed over denominator 3 end fraction fraction numerator 9 J squared over denominator m squared L squared end fraction end cell end table$

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