A) TTFT
B) FTFT
C) FTTT
D) FFTF
Correct Answer: B
Solution :
\[{{\text{S}}_{\text{1}}}\]: No work is done by net force, it only changes direction of momentum of particle. Hence \[{{\text{S}}_{\text{1}}}\] is false. \[{{\text{S}}_{2}}\]: True by definition. \[{{\text{S}}_{3}}\]: Nothing is said about acceleration of both particles. Hence angle between velocity and -acceleration of centre of mass may not be zero. Consequently centre of mass may not move along a straight line. Hence \[{{\text{S}}_{3}}\]is false. \[{{\text{S}}_{4}}\]: \[{{\vec{V}}_{cm}}=\frac{{{m}_{1}}{{{\vec{v}}}_{1}}+{{m}_{2}}{{{\vec{v}}}_{2}}+.....+{{m}_{n}}{{{\vec{v}}}_{n}}}{{{m}_{1}}+{{m}_{2}}+.....+{{m}_{n}}}\] \[=\frac{{{{\vec{F}}}_{net}}}{({{m}_{1}}+{{m}_{2}}+.....+{{m}_{n}})}\] Direction at \[{{\vec{P}}_{net}}\]is fixed so \[{{\vec{V}}_{cm}}\]is also constant in the direction. So path of CM will be straight line.
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