A) The other end also moves uniformly
B) The speed of other end goes on decreasing
C) The speed of other end goes on increasing
D) The speed of other end first decreases and then increases
Correct Answer: B
Solution :
[b] \[{{v}_{x}}=\frac{dx}{dt}=\frac{dy}{dt}.\frac{dx}{dy}\] Since \[x=\sqrt{{{\ell }^{2}}-{{y}^{2}}}\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{dx}{dy}=-\frac{y}{\sqrt{{{\ell }^{2}}-{{y}^{2}}}}\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{v}_{x}}=-\frac{y}{\sqrt{{{\ell }^{2}}-{{y}^{2}}}}.\frac{dy}{dt}=\frac{y+|{{v}_{y}}|}{\sqrt{{{\ell }^{2}}-{{y}^{2}}}}\] Thus, the speed of the lower end gets smaller and smaller and vanishes at\[y=0\].
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