A uniform rod of length L and mass M is lying on a frictionless horizontal plane and is pivoted at one of its ends as shown in figure. There is no friction at the pivot. An inelastic ball of mass m is fixed with the rod at a distance L/3 from O. A horizontal impulse J is given to the rod at a distance 2L/3 from O in a direction perpendicular to the rod. Assume that the ball remains in contact with the rod after the collision and impulse J acts for a small time interval $\mathrm{\Delta t}$

Now answer the following questions: 

 

Find the resulting instantaneous angular velocity of the rod after the impulse.

• A

  $\frac{3\mathrm{J}}{(\mathrm{m}+3\mathrm{M})\mathrm{L}}$

• B

  $\frac{6\mathrm{J}}{(\mathrm{m}+3\mathrm{M})\mathrm{L}}$

• C

  $\frac{3\mathrm{J}}{(3\mathrm{m}+\mathrm{M})\mathrm{L}}$

• D

  $\frac{6\mathrm{J}}{(3\mathrm{m}+\mathrm{M})\mathrm{L}}$

Find the impulse acted on the ball during the time interval $\mathrm{\Delta t}$.

• A

  $\frac{2\mathrm{MJ}}{(3\mathrm{m}+\mathrm{M})}$

• B

  $\frac{2\mathrm{MJ}}{(\mathrm{m}+3\mathrm{M})}$

• C

  $\frac{2\mathrm{m}\cdot \mathrm{J}}{(3\mathrm{m}+\mathrm{M})}$

• D

  $\frac{2\mathrm{mJ}}{(\mathrm{m}+3\mathrm{M})}$

Find the magnitude of the impulse applied by the pivot during the time interval $\mathrm{\Delta t}$.

• A

  $\frac{\mathrm{mJ}}{(\mathrm{m}+3\mathrm{M})}$

• B

  $\frac{\mathrm{mJ}}{(3\mathrm{m}+\mathrm{M})}$

• C

  $\frac{\mathrm{MJ}}{(\mathrm{m}+3\mathrm{M})}$

• D

  $\frac{\mathrm{MJ}}{(3\mathrm{m}+\mathrm{M})}$

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