A) \[{{v}_{_{x}}}<0,\,{{V}_{y}}<0\]
B) \[{{v}_{_{x}}}>0,\,{{V}_{y}}>0\]
C) \[x{{v}_{x}}+y{{v}_{y}}>0\]
D) \[x{{v}_{x}}+y{{v}_{y}}<0\]
Correct Answer: D
Solution :
The object is definitely moving towards 0 when the velocity of the particle v is directed towards O, i.e., the directions of v and r are opposite to each other; so, the value of r . v must be negative or, \[\vec{r}.\vec{v}=(x\hat{i}+y\hat{i}).({{v}_{x}}\hat{i}+{{v}_{y}}\hat{j})<0\] \[=x{{v}_{x}}+y{{v}_{y}}<0\] Hence, the correction option is .
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