A) \[\frac{Mgx}{l}\]
B) \[\frac{2Mgx}{l}\]
C) \[\frac{3Mgx}{l}\]
D) \[\frac{4Mgx}{l}\]
Correct Answer: C
Solution :
[c]: Mass per unit length, \[\lambda =\frac{M}{l}.\] The descending part of the chain is in free fall, also its every point has descended by a distance x. So, speed of each point, \[v=\sqrt{2gx}\] Assume a very small distance dx falls in a short internal of time dt. Normal exerted on the falling part, \[N=-\frac{d{{p}_{x}}}{dt}=\frac{-(0-(\lambda dx)v)}{dt}\] \[=\lambda {{v}^{2}}=\lambda (2gx)=2\lambda gx\] Normal due to x part of the chain on the weighing machine, \[N'=\lambda gx\] Reading of the scale \[W=N+N'=3\lambda gx\]You need to login to perform this action.
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