A) \[\frac{M}{3}\]
B) \[\frac{3M}{4}\]
C) \[\frac{M}{4}\]
D) \[\frac{2M}{3}\]
Correct Answer: C
Solution :
[c] When ball A is at its lowest position, let the stretch in the spring be x. At this instant tension acting on B is kx. \[\therefore \,\,\,\,N=Mg-T\] For N to be equal to \[\frac{Mg}{2}\Rightarrow T=\frac{Mg}{2}\] \[\therefore \] The spring must stretch by x such that \[kx=\frac{Mg}{2}\] (when A comes to rest) Energy Conservation: Loss in PE of A = Gain in spring PE \[mgx=\frac{1}{2}k{{x}^{2}}\,\,\,\Rightarrow \,\,\,x=\frac{2mg}{k}\] \[kx=2mg\Rightarrow \frac{mg}{2}=2mg\] \[\therefore \,\,\,\,m=\frac{M}{4}\]You need to login to perform this action.
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