A rod of length 'L' is hung from its one end and a mass 'm' is attached to its free end. What tangential…

A rod of length 'L' is hung from its one end and a mass 'm' is attached to its free end. What tangential velocity must be imparted to 'm', so that it reaches the top of the vertical circle? (g = acceleration due to gravity)
  1. $4 \sqrt{\mathrm{gL}}$
  2. $2 \sqrt{\mathrm{gL}}$
  3. $5 \sqrt{\mathrm{gL}}$
  4. $3 \sqrt{\mathrm{gL}}$

Solution

$2 \sqrt{g L}$ $h=2 L$ $\frac{1}{2} \mathrm{mv}^{2}=\mathrm{mg} 2 \mathrm{L}$ $v_{2}=4 g L$ $v=2 \sqrt{g L}$

Asked in: MHT CET 2020 (20 Oct Shift 1)

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