A) \[(1,\,\,1)\]
B) \[(0,\,\,0)\]
C) \[(9,\,\,2)\]
D) \[(3,\,\,3)\]
Correct Answer: B
Solution :
For perimeter to be minimum, AM + BM should be minimum. \[\frac{1}{{{k}_{s}}}=\frac{1}{k}\,\left( \frac{1}{1-1/2} \right)\] AB is fixed) For AM + BM to be minimum. M should be such that AM is reflected along MB from the line \[\Rightarrow \] \[\frac{1}{{{k}_{s}}}=\frac{2}{k}\Rightarrow \,{{k}_{s}}=\frac{k}{2}\] [C is reflection of A on line \[\Rightarrow \] i.e. \[T=2\pi \sqrt{\frac{m}{{{k}_{s}}}}\,\Rightarrow \,T=2\pi \sqrt{\frac{2m}{k}}\] So, the equation of CB is \[{{f}_{approach}}=\left( \frac{v}{v-{{v}_{s}}} \right)\,{{f}_{0}}={{f}_{0}}={{f}_{1}}\]. \[{{f}_{recede}}=\left( \frac{v}{v+{{v}_{s}}} \right){{f}_{0}}={{f}_{2}}\,(<{{f}_{1}})\] \[{{Q}_{1}}+(-{{W}_{1}})={{Q}_{2}}+(-{{W}_{2}})={{U}_{B}}-{{U}_{A}}\]You need to login to perform this action.
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