question_answer

Three different objects of masses \[F=-\frac{{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}}y\] and \[\frac{{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}}\] are allowed to fall from rest and from the same point O along three different frictionless paths. The speeds of three objects on reaching the ground will be:

A) \[n=\frac{1}{2\pi }\sqrt{\frac{{{k}_{1}}{{k}_{2}}}{({{k}_{1}}+{{k}_{2}})m}}\]          

B)       \[\frac{1}{k}=\frac{1}{{{k}_{1}}}+\frac{1}{{{k}_{2}}}\]                     

C) \[k=\frac{{{k}_{1}}{{k}_{2}}}{{{k}_{1}}+{{k}_{2}}}\]          

D)       \[n=\frac{1}{2\pi }\sqrt{\frac{k}{m}}\]