Question

A long slender rod of mass $2kg$ and length $4m$ is placed on a smooth horizontal table. Two particles of masses $2kg$ and $1kg$ strike the rod simultaneously and stick to the rod after collision as shown in Figure.
If the two particles strike the rod in opposite direction, then after collision, as compared to the previous situation the rod will

• A. Rotate faster but translate at the same rate
• B. Show no change in linear or angular velocity
• C. Rotate slower and translate faster
• D. Rotate faster and translate slower

Answer 1

The correct option is D Rotate faster and translate slower

The rod rotates faster since we have large initial angular momentum

$I_0=20+10=30$

$L_0=L_{0previous}$

We have smaller initial linear momentum

$P_0=2\times 10-1\times 10=10㎏/s$ ($<P_{0previous}$