question_answer

For a system of two springs and block system, choose the correct option.

A)  for the equilibrium position (about which oscillation occur), the stretch is\[x=\frac{mg}{k}\]

B)  the time period of oscillation is\[2\pi \sqrt{\frac{m}{2k}}\]

C)  Both [a] and [b] are correct                                                               

D)  Both [c] and [b] are incorrect                                                                

Correct Answer: B

Solution :

 Idea When spring of spring constants\[{{k}_{1}},{{k}_{2}},{{k}_{3}}...\]are connected in parallel then their   equivalent   spring constant is given by \[{{k}_{eq}}={{k}_{1}}+{{k}_{2}}+{{k}_{3}}...\] 2kx = mg \[\Rightarrow \]\[x=\frac{mg}{2k}\] As springs are in parallel. \[\therefore \]\[{{k}_{eq}}=k+k=2k\] So, \[T=2\pi \sqrt{\frac{m}{{{k}_{eq}}}}\] \[T=2\pi \sqrt{\frac{m}{2k}}\] TEST Edge Question related to series combination of springs can also be asked in that case \[\frac{1}{{{k}_{eq}}}=\frac{1}{{{k}_{1}}}+\frac{1}{{{k}_{2}}}+\frac{1}{{{k}_{3}}}...\] However, case may also arise in which both series and parallel combination is given.