question_answer

In the arrangement shown in the figure, block B of mass M rests on a weighing scale. Ball A is released from a position where spring is in its natural length and the scale shows the correct weight of block B. Find the mass of ball A so that the minimum reading shown by the scale subsequently is half the true weight of B.

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 \[mgx=\frac{1}{2}k{{x}^{2}}\,\,\,\Rightarrow \,\,\,x=\frac{2mg}{k}\] \[kx=2mg\Rightarrow \frac{mg}{2}=2mg\]    \[\therefore \,\,\,\,m=\frac{M}{4}\]