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QJEEAdv20Phc26c: JEE Advanced 2020 Physics - Class 11 JEEAdv20Phc26c Solution: A rod of mass m and length L, pivoted at one of its ends, is…

A rod of mass m and length L, pivoted at one of its ends, is hanging vertically. A bullet of the same mass moving at speed v strikes the rod horizontally at a distance x from its pivoted end and gets embedded in it. The combined system now rotates with angular speed ω about the pivot. The maximum angular speed ωM is achieved for x = xM. Then

JEE Advanced 2020 Paper 2 Offline Physics - Rotational Motion Question 38 English

Multiple Choice Options

  • A ω=3vxL2+3x2
  • B ω=12vxL2+12x2
  • C xM=L3
  • D ωM=v2L3

Step-by-Step Verified Solution

According to conservation of angular momentum about suspension point,

mvx=(mL23+mx2)ω

vx=(L23+x2)ω⇒ω=3vxL2+3x2

For maximum,

dωdx=0⇒x=L3⇒ω=3v2L

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