1.

Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities omega_(1) and omega_(2) . They are brought into contact face to face coinciding the axis of rotation . The expression for loss of energy during this process is

Answer» <html><body><p>`(1)/(4) I (omega_1 - omega_2)^(2)`<br/>`I (omega_(1) - omega_(2))^(2)`<br/>`(1)/(8) I (omega_(1) - omega_(2))^(2)`<br/>`(1)/(2) I (omega_(1)+ omega_(2))^(2)`</p>Solution :Initial angular momentum = `I omega_(1) + I omega_(2)` <br/> Let `omega` be angular speed of the combined system . <br/> Final angular momentum = `2 I omega` <br/> Final angular momentum = `2 I omega` <br/> `<a href="https://interviewquestions.tuteehub.com/tag/therefore-706901" style="font-weight:bold;" target="_blank" title="Click to know more about THEREFORE">THEREFORE</a>` According to conservation of angular momentum `I omega_(1) + I omega_(2) = 2 I omegaor omega = (omega_(1) + omega_(2))/(2)` <br/> Initial <a href="https://interviewquestions.tuteehub.com/tag/rotational-625601" style="font-weight:bold;" target="_blank" title="Click to know more about ROTATIONAL">ROTATIONAL</a> <a href="https://interviewquestions.tuteehub.com/tag/kinetic-533291" style="font-weight:bold;" target="_blank" title="Click to know more about KINETIC">KINETIC</a> <a href="https://interviewquestions.tuteehub.com/tag/energy-15288" style="font-weight:bold;" target="_blank" title="Click to know more about ENERGY">ENERGY</a> , `E_(1) = (1)/(2) I (omega_(1)^(2) + omega_(2)^(2))` <br/> Final rotational kinetic energy <br/> `E_(<a href="https://interviewquestions.tuteehub.com/tag/f-455800" style="font-weight:bold;" target="_blank" title="Click to know more about F">F</a>) = (1)/(2) (2 I) omega^(2) = (1)/(2) (2I) ((omega_(1) + omega_(2))/(2))^(2) = (1)/(4) I (omega_(1) + omega_(2))^(2)` <br/> `therefore` Loss of energy `Delta E= E_(i) - E_(f)` <br/> `= (1)/(2) (omega_(1)^(2) + omega_(2)^(2))- (1)/(4) (omega_(1)^(2) + omega_(2) ^(2) + 2omega_(1) omega_(2))` <br/> `= (1)/(4) [ omega_(1)^(2) + omega_(2) ^(2) - 2 omega_(1) omega_(2)] = (1)/(4) (omega_(1) - omega_(2))^(2)`</body></html>


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