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Mechanics — Hard JEE physics MCQ

A bar of mass $M=1.00 \mathrm{~kg}$ and length $L=0.20 \mathrm{~m}$ is lying on a horizontal frictionless surface. One end of the bar is pivoted at a point about which it is free to rotate. A small mass $m=0.10 \mathrm{~kg}$ is moving on the same horizontal surface with $5.00 \mathrm{~m} \mathrm{~s}^{-1}$ speed on a path perpendicular to the bar. It hits the bar at a distance $L / 2$ from the pivoted end and returns back on the same path with speed $\mathrm{v}$. After this elastic collision, the bar rotates with an angular velocity $\omega$. Which of the following statement is correct?
  1. A. $\omega=6.98 \mathrm{rad} \mathrm{s}^{-1}$ and $\mathrm{v}=4.30 \mathrm{~m} \mathrm{~s}^{-1}$
  2. B. $\omega=3.75 \mathrm{rad} \mathrm{s}^{-1}$ and $\mathrm{v}=4.30 \mathrm{~m} \mathrm{~s}^{-1}$
  3. C. $\omega=3.75 \mathrm{rad} \mathrm{s}^{-1}$ and $\mathrm{v}=10.0 \mathrm{~m} \mathrm{~s}^{-1}$
  4. D. $\omega=6.80 \mathrm{rad} \mathrm{s}^{-1}$ and $\mathrm{v}=4.10 \mathrm{~m} \mathrm{~s}^{-1}$

Solution

The correct option is **A**.

PHYSICS

hard • PYQ Reworded
Question
Read carefully, then pick the best option.
A bar of mass M=1.00 kgM=1.00 \mathrm{~kg} and length L=0.20 mL=0.20 \mathrm{~m} is lying on a horizontal frictionless surface. One end of the bar is pivoted at a point about which it is free to rotate. A small mass m=0.10 kgm=0.10 \mathrm{~kg} is moving on the same horizontal surface with 5.00 m s−15.00 \mathrm{~m} \mathrm{~s}^{-1} speed on a path perpendicular to the bar. It hits the bar at a distance L/2L / 2 from the pivoted end and returns back on the same path with speed v\mathrm{v}. After this elastic collision, the bar rotates with an angular velocity ω\omega. Which of the following statement is correct?
AI hints
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