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Byju's Answer

Standard XII

Physics

Angular Analogue of Linear Momentum

A bar of mass...

Question

A bar of mass $M$ and length $L$ is in pure translatory motion with its centre of mass velocity $V$ . It collides with and sticks to a second identical bar which is initially at rest. (Assume that it becomes one composite bar of length $2 L$ ). The angular velocity of the composite bar will be

3 V / 4 L

clockwise

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4 V / 3 L

clockwise

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3 V / 4 L

counter clockwise

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V / L

counter clockwise

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Solution

The correct option is C $3 V / 4 L$ counter clockwise
By law of conservation of angular momentum
$\sum m v r = (I_{s y s t e m}) w$
$\Rightarrow \frac{1}{2} m v = \frac{(2 m) {(2 l)}^{2}}{12} w = \frac{2 m ({4 l}^{2})}{12} w$
$\Rightarrow w = \frac{3 v}{4 l} (a n t i - c l o c k w i s e)$

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A bar of mass M and length L is in pure translatory motion with its centre of mass velocity V. It collides with and sticks to a second identical bar which is initially at rest. (Assume that it becomes one composite bar of length 2L). The angular velocity of the composite bar will be

The correct option is C 3V/4L counter clockwiseBy law of conservation of angular momentum∑mvr=(Isystem)w⇒12mv=(2m)(2l)212w=2m(4l2)12w⇒w=3v4l(anti−clockwise)

A bar of mass $M$ and length $L$ is in pure translatory motion with its centre of mass velocity $V$ . It collides with and sticks to a second identical bar which is initially at rest. (Assume that it becomes one composite bar of length $2 L$ ). The angular velocity of the composite bar will be

The correct option is C $3 V / 4 L$ counter clockwise
By law of conservation of angular momentum
$\sum m v r = (I_{s y s t e m}) w$
$\Rightarrow \frac{1}{2} m v = \frac{(2 m) {(2 l)}^{2}}{12} w = \frac{2 m ({4 l}^{2})}{12} w$
$\Rightarrow w = \frac{3 v}{4 l} (a n t i - c l o c k w i s e)$