COMEDK · Physics · 8. Rotational Motion
A bullet, fired into a door gets embedded exactly at it's centre, causing the door to rotate about it's vertical axis, practically without friction, with an angular velocity of \(0.625\ rads^{-1}\). The door is 1.0 m wide and weighs 12 kg. If the mass of the bullet is 10g, find the speed with which it was fired. (Hint: The moment of inertia of the door about the vertical axis at one end is \(\dfrac{ML^2}{3}\)).
- A \(342\ ms^{-1}\)
- B \(645\ ms^{-1}\)
- C \(500\ ms^{-1}\)
- D \(124\ ms^{-1}\)
Answer & Solution
Correct Answer
(C) \(500\ ms^{-1}\)
Step-by-step Solution
Detailed explanation
By conservation of angular momentum about the vertical axis of the door: \(L_i = L_f\) \(m v r = (I_{door} + I_{bullet}) \omega\) \(m v \left(\dfrac{L}{2}\right) = \left(\dfrac{ML^2}{3} + m\left(\dfrac{L}{2}\right)^2\right) \omega\) Substituting the given values \(M = 12\ kg\),…
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